SAT Math

Answer: A - The product of solutions for which quadratic equation has one solution is − 15. Solve for k in the equation D = 0, where D is the discriminant of the quadratic equation.
x^2 − (k − 1)x + 4 = 0
a = 1,b = − (k − 1),c = 4
D = b^2 − 4ac = [ − (k − 1)]^2 − 4 × 1 × 4 = (k − 1)^2 − 16 = k^2 − 2k + 1 − 16 =
= k^2 − 2k − 15
D = 0
k^2 − 2k − 15 = 0
k^2 − 2k − 15 = k^2 − 5k + 3k − 15 = k(k − 5) + 3(k − 5) = (k − 5)(k + 3)
(k − 5)(k + 3) = 0
k_1 = 5,k_2 = − 3

The product of solutions for which the quadratic equation has one solution is 5 × ( − 3) = − 15.