sat suite question viewer

Advanced Math / Nonlinear equations in one variable and systems of equations in two variables Difficulty: Easy

$3 x^{2} - 15 x + 18 = 0$

How many distinct real solutions are there to the given equation?

Back question 139 of 148 Next

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148

Explanation

Choice B is correct. The number of solutions to a quadratic equation of the form $a x^{2} + b x + c = 0$ , where $a$ , $b$ , and $c$ are constants, can be determined by the value of the discriminant, $b squared minus 4 a c$ . If the value of the discriminant is positive, then the quadratic equation has exactly two distinct real solutions. If the value of the discriminant is equal to zero, then the quadratic equation has exactly one real solution. If the value of the discriminant is negative, then the quadratic equation has zero real solutions. In the given equation, $3 x^{2} - 15 x + 18 = 0$ , $a equals 3$ , $b = - 15$ , and $c equals 18$ . Substituting $3$ for $a$ , $negative 15$ for $b$ , and $18$ for $c$ in $b squared minus 4 a c$ yields $(- 15)^{2} - 4 (3) (18)$ , or $9$ . Since the value of the discriminant is positive, the given equation has exactly two distinct real solutions.

Choice A is incorrect and may result from conceptual or calculation errors.

Choice C is incorrect and may result from conceptual or calculation errors.

Choice D is incorrect and may result from conceptual or calculation errors.