Intermediate Algebra

Quadratic Equations

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MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Use the zero-factor property to solve the equation.1) x2 + 7x + 6 = 0 1)

A) {0, 6} B) {-6, 0} C) {-6, -1} D) {1, 6}

2) 2x2 + x - 15 = 0 2)

A) -3, 52

B) -3, -52

C) 52

, 3 D) -52

, 3

3) x2 = 10x - 24 3)A) {4, 6} B) {-4, -6} C) {-24, -1} D) {1, 24}

Use the square root property to solve the equation.4) x2 = 49 4)

A) {7, -7} B) {24.5} C) {8, -8} D) {7}

5) x2 - 4 = 0 5)A) {2} B) {2, -2} C) {4.5} D) {1, -1}

6) (x + 4)2 = 25 6)A) {-29} B) {-9, 1} C) {9, -1} D) {1}

7) (3s + 8)2 = 36 7)

A) -23

, -143

B) -23

, 0 C) 23

, 143

D) 283

Solve the equation by completing the square.8) a2 - 10a + 21 = 0 8)

A) {18, 3} B) {7, 3} C) {-7, -3} D) {5, - 5}

9) z2 + 16z + 44 = 0 9)A) 8 + 2 5 B) 8 + 2 11, 8 - 2 11C) -16 + 2 11 D) -8 + 2 5, -8 - 2 5

10) 0.1x2 - 0.2x - 0.5 = 0 10)A) {1 + 6, 1 - 6} B) {2 - 6} C) {2 + 6, 2 - 6} D) {1 + 6}

Find the nonreal complex solutions of the equation.11) x2 - 4x + 20 = 0 11)

A) {2 + 4i, 2 - 4i} B) {6, -2} C) {4 + 8i, 4 - 8i} D) {-2 + 4i, -2 - 4i}

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12) x2 + 4x + 53 = 0 12)A) {-2 + 7i, -2 - 7i} B) {5, -9}C) {2 + 7i, 2 - 7i} D) {-2 + 53i, -2 - 53i}

Use the quadratic formula to solve the equation. (All solutions are real numbers.)13) 2n2 = -10n - 7 13)

A) -10 + 112

, -10 - 112

B) -5 + 392

, -5 - 392

C) -5 + 112

, -5 - 112

D) -5 + 114

, -5 - 114

14) z23

=z2

+56

14)

A) 52

B) -1, 52

C) {-1} D) 3 + 2 104

, 3 - 2 104

Use the quadratic formula to solve the equation.15) x2 + x + 4 = 0 15)

A) 1 + i 152

, 1 - i 152

B) 1 + 152

, 1 - 152

C) -1 + i 152

, -1 - i 152

D) -1 + 152

, -1 - 152

16) 8x2 + 7x = -2 16)

A) 7 + i 1516

, 7 - i 1516

B) -7 + 1516

, -7 - 1516

C) -7 + i 1516

, -7 - i 1516

D) 7 + 1516

, 7 - 1516

Use the discriminant to determine whether the equation has two rational solutions, one rational solution, two irrationalsolutions, or two nonreal complex solutions. Do not actually solve.

17) s2 + 3s - 4 = 0 17)A) Two nonreal complex solutions B) One rational solutionC) Two irrational solutions D) Two rational solutions

18) t2 + 8t + 16 = 0 18)A) Two irrational solutions B) One rational solutionC) Two rational solutions D) Two nonreal complex solutions

19) 4y2 = 6y - 7 19)A) Two irrational solutions B) One rational solutionC) Two nonreal complex solutions D) Two rational solutions

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