Question

Which of the following is the solution of the equation \(-4 x^{2}+24 x-36=0 ?\) A) -6 B) -3 C) 2 D) 3

Short answer

The solution of the equation is D) 3.

Step-by-step solution

Identify the coefficients

In the equation \(-4x^2 + 24x - 36 = 0\), the coefficients are a = -4, b = 24, and c = -36.

Apply the quadratic formula

Substitute these coefficients into the quadratic formula: \(x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\). This gives the calculation \(x = \frac{-24 \pm \sqrt{24^2 - 4(-4)(-36)}}{2(-4)}\).

Simplify the expression

When simplified, the expression becomes \(x = \frac{-24 \pm \sqrt{576 - 576}}{-8}\). Note that the discriminant, which is the expression inside the square root, comes out to be zero.

Compute the roots

The roots of the equation are given by \(x = \frac{-24 \pm 0}{-8}\), which simplifies to \(x = 3\).