Determine the number of real solutions of $36 x ^ { 2 } - 12 x + 61 = 0$ by using the discriminant.
A)2
B)1
C)none

Question

Quizplus · Accepted Answer

The discriminant of a quadratic equation $ax^2 + bx + c = 0$ is given by $D = b^2 - 4ac$. For the given equation, $a = 36$, $b = -12$, and $c = 61$. Thus, $D = (-12)^2 - 4(36)(61) = 144 - 8784 = -8640$. Since the discriminant is negative, the equation has no real solutions.

Determine the Number of Real Solutions Of 36x2−12x+61=036 x ^ { 2 } - 12 x + 61 = 036x2−12x+61=0

Determine the Number of Real Solutions Of $36 x ^ { 2 } - 12 x + 61 = 0$