Determine the discriminant. Then use it to determine the number of x-intercepts that the function has. $$m ( x ) = - 3 x ^ { 2 } + 8 x - 9$$
A) Discriminant: -44; no x-intercepts
B) Discriminant: -44; two x-intercepts
C) Discriminant: -172; no x-intercepts
D) Discriminant: -172; two x-intercepts

Question

Quizplus · Accepted Answer

The discriminant of a quadratic equation in the form $ax^2 + bx + c = 0$ is given by $b^2 - 4ac$. For the given function $m(x) = -3x^2 + 8x - 9$, $a = -3$, $b = 8$, and $c = -9$. Thus, the discriminant is $8^2 - 4(-3)(-9) = 64 - 108 = -44$. A negative discriminant means the quadratic equation has no real roots, hence no x-intercepts.

Determine the Discriminant m(x)=−3x2+8x−9m ( x ) = - 3 x ^ { 2 } + 8 x - 9m(x)=−3x2+8x−9

Determine the Discriminant $m ( x ) = - 3 x ^ { 2 } + 8 x - 9$