Exam 11: Quadratic Equations and Inequalities

Use the discriminant to determine whether the equation has two nonreal complex solutions, one real solution with a multiplicity of two, or two real solutions. y 2 $-$ 6 y $-$ 27 = 0

Free

(Multiple Choice)

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Question 1

Correct Answer:

Verified

A

Use the method of completing the square to solve the quadratic equation. 3 x 2 + 5 x $-$ 1 = 0

Free

(Multiple Choice)

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Question 2

Correct Answer:

Verified

B

Find two numbers such that their sum is 8 and their product is 7. Please enter your answer as two numbers, separated by a comma.

Free

(Short Answer)

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Question 3

Correct Answer:

Verified

1, 7

Solve each quadratic equation by using the method of completing the square. Match each equation with the corresponding solution. - $x = - 2 , x = 4$

(Multiple Choice)

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Question 4

Find the quotient $\frac { - 2 + 16 i } { - 1 + i }$ and express the answer in the standard form of a complex number.

(Short Answer)

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Question 5

For this problem a and b represent the lengths of the legs of a right triangle, and c represents the length of the hypotenuse. Find c if a = 16 centimeters and b = 24 centimeters. Express the answer in simplest radical form.

(Short Answer)

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Question 6

Use the quadratic formula to solve the quadratic equation. 20 y 2 $-$ 181 y + 399 = 0 Please enter your answer as fractions and/or two numbers, separated by a comma.

(Short Answer)

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Question 7

Solve the inequality. ( x + 4 )( x $-$ 2 ) 0 Please enter your answer in interval notation.

(Short Answer)

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Question 8

Write $\sqrt { - 3 } \sqrt { - 81 }$ in terms of i , perform the indicated operations, and simplify.

(Short Answer)

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Question 9

Solve each quadratic equation using the method that seems most appropriate. 2( x + 1 ) ² + 1 = 15

(Multiple Choice)

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Question 10

Add or subtract as indicated. ( $-$ 3 $-$ 9 i ) + (4 $-$ 6 i )

(Short Answer)

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Question 11

Solve the quadratic equation using the method that seems most appropriate to you. $x ^ { 2 } - 4 x - 19 = 0$ Please enter your answer as two numbers, separated by a comma.

(Short Answer)

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Question 12

Use the discriminant to determine whether the equation has two nonreal complex solutions, one real solution with a multiplicity of two, or two real solutions. $x ^ { 2 } - 5 x - 50 = 0$

(Short Answer)

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Question 13

A perfect-square trinomial is the product of the square of a binomial.

(True/False)

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Question 14

Solve the inequality. $( 3 x - 2 ) ( 4 x + 9 ) \geq 0$

(Multiple Choice)

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Question 15

Use the quadratic formula to solve the quadratic equation. x 2 + 4 x $-$ 21 = 0 Please enter your answer as fractions and/or two numbers, separated by a comma.

(Short Answer)

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Question 16

The length of a rectangular floor is 8 meter less than twice its width. If a diagonal of the rectangle is 20 meters, find the length and width of the floor.

(Multiple Choice)

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Question 17

Solve each quadratic equation by using the method of completing the square. Match each equation with the corresponding solution. - $x = - 5 , x = 7$

(Multiple Choice)

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Question 18

Solve the quadratic equation. $14 n ^ { 2 } = 36$

(Short Answer)

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Question 19

Use the method of completing the square to solve the quadratic equation. x 2 + 6 x $-$ 6 = 0 Please enter your answer as two numbers, separated by a comma.

(Short Answer)

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(76)

Question 20

Use the discriminant to determine whether the equation has two nonreal complex solutions, one real solution with a multiplicity of two, or two real solutions. y 2 $-$ 6 y $-$ 27 = 0

Use the method of completing the square to solve the quadratic equation. 3 x 2 + 5 x $-$ 1 = 0

Find two numbers such that their sum is 8 and their product is 7. Please enter your answer as two numbers, separated by a comma.

Solve each quadratic equation by using the method of completing the square. Match each equation with the corresponding solution. - $x = - 2 , x = 4$

Find the quotient $\frac { - 2 + 16 i } { - 1 + i }$ and express the answer in the standard form of a complex number.

For this problem a and b represent the lengths of the legs of a right triangle, and c represents the length of the hypotenuse. Find c if a = 16 centimeters and b = 24 centimeters. Express the answer in simplest radical form.

Use the quadratic formula to solve the quadratic equation. 20 y 2 $-$ 181 y + 399 = 0 Please enter your answer as fractions and/or two numbers, separated by a comma.

Solve the inequality. ( x + 4 )( x $-$ 2 ) 0 Please enter your answer in interval notation.

Write $\sqrt { - 3 } \sqrt { - 81 }$ in terms of i , perform the indicated operations, and simplify.

Solve each quadratic equation using the method that seems most appropriate. 2( x + 1 ) ² + 1 = 15

Add or subtract as indicated. ( $-$ 3 $-$ 9 i ) + (4 $-$ 6 i )

Solve the quadratic equation using the method that seems most appropriate to you. $x ^ { 2 } - 4 x - 19 = 0$ Please enter your answer as two numbers, separated by a comma.

Use the discriminant to determine whether the equation has two nonreal complex solutions, one real solution with a multiplicity of two, or two real solutions. $x ^ { 2 } - 5 x - 50 = 0$

A perfect-square trinomial is the product of the square of a binomial.

Solve the inequality. $( 3 x - 2 ) ( 4 x + 9 ) \geq 0$

Use the quadratic formula to solve the quadratic equation. x 2 + 4 x $-$ 21 = 0 Please enter your answer as fractions and/or two numbers, separated by a comma.

The length of a rectangular floor is 8 meter less than twice its width. If a diagonal of the rectangle is 20 meters, find the length and width of the floor.

Solve each quadratic equation by using the method of completing the square. Match each equation with the corresponding solution. - $x = - 5 , x = 7$

Solve the quadratic equation. $14 n ^ { 2 } = 36$

Use the method of completing the square to solve the quadratic equation. x 2 + 6 x $-$ 6 = 0 Please enter your answer as two numbers, separated by a comma.

Some Basic Concepts of Arithmetic and Algebra

The Real Numbers

Equations, Inequalities and Problem Solving

Formulas and Problem Solving

Coordinate Geometry and Linear Systems

Exponents and Polynomials

Factoring, Solving Equations and Problem Solving

A Transition From Elementary Algebra to Intermediate Algebra

Rational Expressions

Exponents and Radicals

Coordinate Geometry: Lines, Parabolas, Circles, Ellipses and Hyperbolas

Functions

Exponential and Logarithmic Functions

Systems of Equations: Matrices and Determinants

Filters

Exam 11: Quadratic Equations and Inequalities

Use the discriminant to determine whether the equation has two nonreal complex solutions, one real solution with a multiplicity of two, or two real solutions. y 2 −-− 6 y −-− 27 = 0

Use the method of completing the square to solve the quadratic equation. 3 x 2 + 5 x −-− 1 = 0

Find two numbers such that their sum is 8 and their product is 7. Please enter your answer as two numbers, separated by a comma.

Solve each quadratic equation by using the method of completing the square. Match each equation with the corresponding solution. - x=−2,x=4x = - 2 , x = 4x=−2,x=4

Find the quotient −2+16i−1+i\frac { - 2 + 16 i } { - 1 + i }−1+i−2+16i​ and express the answer in the standard form of a complex number.

For this problem a and b represent the lengths of the legs of a right triangle, and c represents the length of the hypotenuse. Find c if a = 16 centimeters and b = 24 centimeters. Express the answer in simplest radical form.

Use the quadratic formula to solve the quadratic equation. 20 y 2 −-− 181 y + 399 = 0 Please enter your answer as fractions and/or two numbers, separated by a comma.

Solve the inequality. ( x + 4 )( x −-− 2 ) 0 Please enter your answer in interval notation.

Write −3−81\sqrt { - 3 } \sqrt { - 81 }−3​−81​ in terms of i , perform the indicated operations, and simplify.

Solve each quadratic equation using the method that seems most appropriate. 2( x + 1 ) 2 + 1 = 15

Add or subtract as indicated. ( −-− 3 −-− 9 i ) + (4 −-− 6 i )

Solve the quadratic equation using the method that seems most appropriate to you. x2−4x−19=0x ^ { 2 } - 4 x - 19 = 0x2−4x−19=0 Please enter your answer as two numbers, separated by a comma.

Use the discriminant to determine whether the equation has two nonreal complex solutions, one real solution with a multiplicity of two, or two real solutions. x2−5x−50=0x ^ { 2 } - 5 x - 50 = 0x2−5x−50=0

A perfect-square trinomial is the product of the square of a binomial.

Solve the inequality. (3x−2)(4x+9)≥0( 3 x - 2 ) ( 4 x + 9 ) \geq 0(3x−2)(4x+9)≥0

Use the quadratic formula to solve the quadratic equation. x 2 + 4 x −-− 21 = 0 Please enter your answer as fractions and/or two numbers, separated by a comma.

The length of a rectangular floor is 8 meter less than twice its width. If a diagonal of the rectangle is 20 meters, find the length and width of the floor.

Solve each quadratic equation by using the method of completing the square. Match each equation with the corresponding solution. - x=−5,x=7x = - 5 , x = 7x=−5,x=7

Solve the quadratic equation. 14n2=3614 n ^ { 2 } = 3614n2=36

Use the method of completing the square to solve the quadratic equation. x 2 + 6 x −-− 6 = 0 Please enter your answer as two numbers, separated by a comma.

Some Basic Concepts of Arithmetic and Algebra

The Real Numbers

Equations, Inequalities and Problem Solving

Formulas and Problem Solving

Coordinate Geometry and Linear Systems

Exponents and Polynomials

Factoring, Solving Equations and Problem Solving

A Transition From Elementary Algebra to Intermediate Algebra

Rational Expressions

Exponents and Radicals

Coordinate Geometry: Lines, Parabolas, Circles, Ellipses and Hyperbolas

Functions

Exponential and Logarithmic Functions

Systems of Equations: Matrices and Determinants

Filters

Use the discriminant to determine whether the equation has two nonreal complex solutions, one real solution with a multiplicity of two, or two real solutions. y 2 $-$ 6 y $-$ 27 = 0

Use the method of completing the square to solve the quadratic equation. 3 x 2 + 5 x $-$ 1 = 0

Solve each quadratic equation by using the method of completing the square. Match each equation with the corresponding solution. - $x = - 2 , x = 4$

Find the quotient $\frac { - 2 + 16 i } { - 1 + i }$ and express the answer in the standard form of a complex number.

Use the quadratic formula to solve the quadratic equation. 20 y 2 $-$ 181 y + 399 = 0 Please enter your answer as fractions and/or two numbers, separated by a comma.

Solve the inequality. ( x + 4 )( x $-$ 2 ) 0 Please enter your answer in interval notation.

Write $\sqrt { - 3 } \sqrt { - 81 }$ in terms of i , perform the indicated operations, and simplify.

Solve each quadratic equation using the method that seems most appropriate. 2( x + 1 ) ² + 1 = 15

Add or subtract as indicated. ( $-$ 3 $-$ 9 i ) + (4 $-$ 6 i )

Solve the quadratic equation using the method that seems most appropriate to you. $x ^ { 2 } - 4 x - 19 = 0$ Please enter your answer as two numbers, separated by a comma.

Use the discriminant to determine whether the equation has two nonreal complex solutions, one real solution with a multiplicity of two, or two real solutions. $x ^ { 2 } - 5 x - 50 = 0$

Solve the inequality. $( 3 x - 2 ) ( 4 x + 9 ) \geq 0$

Use the quadratic formula to solve the quadratic equation. x 2 + 4 x $-$ 21 = 0 Please enter your answer as fractions and/or two numbers, separated by a comma.

Solve each quadratic equation by using the method of completing the square. Match each equation with the corresponding solution. - $x = - 5 , x = 7$

Solve the quadratic equation. $14 n ^ { 2 } = 36$

Use the method of completing the square to solve the quadratic equation. x 2 + 6 x $-$ 6 = 0 Please enter your answer as two numbers, separated by a comma.