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Question : Solve the system of quadratic equations: : 2151612

Examine the discriminant of each equation and determine the nature of the roots.

81) Solve the system of quadratic equations:

y = x^{2} - 8

y = -x^{2}

A) (-2, -4)

B) (2, -4)

C) both A and B

D) no solution

Examine the discriminant of each equation and determine the nature of the roots.

82) x^{2} + 7x - 8 = 0

A) No real solutions

B) One real solution

C) Two real solutions

83) x^{2} + 10x + 25 = 0

A) One real solution

B) Two real solutions

C) No real solutions

84) x^{2} + 3x - 7 = 0

A) No real solutions

B) One real solution

C) Two real solutions

85) x^{2} + 3x + 4 = 0

A) One real solution

B) No real solutions

C) Two real solutions

86) 25x^{2} - 10x + 1 = 0

A) Two real solutions

B) One real solution

C) No real solutions

87) 7x^{2} = 4x - 2

A) No real solutions

B) One real solution

C) Two real solutions

Provide an appropriate response.

88) Find the discriminant of the equation: 3x^{2} - 2x + 5 = 0

A) The discriminant value is 64.

B) The discriminant value is 56.

C) The discriminant value is 0.

D) The discriminant value is -56.

89) If the discriminant of a quadratic has the value of 8, what is the nature of the roots?

A) The equation has no real number roots.

B) The equation has two real number equal roots.

C) The equation has one rational root.

D) The equation has two real number roots.

90) If the discriminant of a quadratic has the value of -8, what is the nature of the roots?

A) The equation has two real number roots.

B) The equation has no real number roots.

C) The equation has one rational root.

D) The equation has two real number equal roots.

91) If the discriminant of a quadratic has the value of 0, what is the nature of the roots?

A) The equation has no real number roots.

B) The equation has two real number equal roots.

C) The equation has two rational, equal, root.

D) The equation has two real number roots.

92) Find the discriminant of the equation: 10 + 4x - x^{2} = 0

A) The discriminant value is 24i.

B) The discriminant value is -24.

C) The discriminant value is 56.

D) The discriminant value is 48.

93) Find the discriminant of the equation: 3x^{2} - 2x + 5 = 0

A) The discriminant value is 0.

B) The discriminant value is 56.

C) The discriminant value is -56.

D) The discriminant value is 64.

94) Under which of the following conditions of k will this quadratic, x^{2} + 8x + k = 0, have real-number, but unequal roots?

A) k ≥ 16

B) k > 16

C) k ≤ 16

D) k < 16

95) Find the discriminant for 2x^{2} - Bx + r^{2} = 0.

A) -B^{2} - 8r^{2 }

B) B^{2} - 8r^{2 }

C) 1 - 8r^{2 }

D) B^{2} - 8

96) Find the discriminant of the equation: 10 + 4x - x^{2} = 0

A) The discriminant value is 24i.

B) The discriminant value is 48.

C) The discriminant value is -24.

D) The discriminant value is 56.

97) Examine the discriminant and find the roots of the equation, rounding to the nearest hundredth if necessary: 12 + 4x - x^{2} = 0

A) x = -2, 6

B) x = 2 + 2.83i, 2 - 2.83i

C) x = 2.42, -0.42

D) x = 2, -6

98) Examine the discriminant and find the roots of the equation, rounding to the nearest hundredth if necessary: 3x^{2} - 2x + 4 = 0

A) x = 1.54, -0.87

B) x = 0.33 + 0.44i, 0.33 - 0.44i

C) x = -0.33 + 1.11i, -0.33 - 1.11i

D) x = 0.33 + 1.11i, 0.33 - 1.11i

99) Examine the discriminant and find the roots of the equation, rounding to the nearest tenth if necessary: 5x^{2} - 6x = -5

A) x = 0.6 ± 0.8i

B) x = 3 ± 4i

C) x = 0.6 ± 1.17i

D) x = 1.4, -0.2

100) Solve the following quadratic equation using any method: x^{2} - 8x + 16 = 0

A) x = -4, -4

B) x = 9.66, -1.66

C) x = 4, 4

D) x = 4, -4

101) Solve the following quadratic equation using any method: 2x^{2} = 50

A) x = 5i, -5i

B) x = 5i

C) x = 5, -5

D) x = 5

102) Solve the following quadratic equation using any method: 4x^{2} = 28x

A) x = 4, 7

B) x = 0, 4, 7

C) x = 0, 7

D) x = 7

103) Under which of the following conditions of k will this quadratic, x^{2} + kx + 36 = 0, have one real root?

A) k = 6

B) k = 6, -6

C) k = 12, -12

D) k = 12

104) Solve the following quadratic equation using any method: 16x^{2} = 49

A) x = (4/7)

B) x = (7/4), - (7/4)

C) x = (4/7), - (4/7)

D) x = (7/4)

105) Solve the following quadratic equation using any method: 0.04x^{2} = 0.25

A) x = 0.16

B) x = 2.5, -2.5

C) x = 6.25

D) x = 0.16, -0.16

106) Under which of the following conditions of k will this quadratic, kx^{2} + 6x + 3 = 0, have nonreal roots?

A) k > 3

B) k = 3

C) k < 3

D) k ≥ 3

107) Solve the following quadratic equation using any method: 6x^{2} - 36x = 0

A) x = 0, -6, 6

B) x = 0, 6

C) x = -6, 6

D) x = 6

108) Solve the following quadratic equation using any method: 10x^{2} + 29x - 21 = 0

A) (7/2), (3/5)

B) (7/2), - (3/5)

C) - (7/2), - (3/5)

D) - (7/2), (3/5)

109) A number multiplied by 196 is the same as four times the cube of the number. What is the number?

A) 7, -7

B) 49, -49

C) 7

D) 49