Question

What value of $k$ will make $4x^2 - 20x + k$ the square of a binomial?

Answer 1

k = 25

Explanation:

(2x - sqrt(k) )^2 Expand this as a binomial

4x^2 - 4x*sqrt(k) + k The middle term must be -20x Solve for k so it is

-4xsqrt(k) = - 20x Divide by -4x

sqrt(k) = -20x/-4x Do the division

sqrt(k) = 5 Square both sides

k = 25