Compute the discriminant. Then determine the number and type of solutions for the given equation.
-$$x ^ { 2 } - 6 x + 9 = 0$$
A) 0 ; one real solution
B) 36 ; two unequal real solutions
C) $- 36$; two complex imaginary solutions

Question

Quizplus · Accepted Answer

The discriminant of a quadratic equation $ax^2 + bx + c = 0$ is given by $b^2 - 4ac$. For the given equation $x^2 - 6x + 9 = 0$, $a = 1$, $b = -6$, and $c = 9$. Thus, the discriminant is $(-6)^2 - 4(1)(9) = 36 - 36 = 0$. A discriminant of 0 indicates that there is exactly one real solution.

Compute the Discriminant x2−6x+9=0x ^ { 2 } - 6 x + 9 = 0x2−6x+9=0

Compute the Discriminant $x ^ { 2 } - 6 x + 9 = 0$