Question

1. what value(s) of b will cause 4x² + bx + 25 = 0 to have one real solution?

□ a -200
□ b -20
□ c -2
□ d 2
□ e 20
□ f 200

Explanation:

Step1: Recall discriminant formula

For quadratic equation \(ax^2 + bx + c = 0\), discriminant \(D = b^2 - 4ac\). One real solution when \(D = 0\).
Here, \(a = 4\), \(c = 25\), so \(D = b^2 - 4\times4\times25 = b^2 - 400\).

Step2: Set discriminant to zero

Set \(D = 0\): \(b^2 - 400 = 0\)
\(b^2 = 400\)
\(b = \pm\sqrt{400} = \pm20\)

Answer:

B. -20, E. 20