Consider the equation 2x2-3x plus k equals 0for what values of m is one root double the other root?

2x2 - 3x + k = 0

a = 2, b = -3, c = k

D = b2 - 4ac = (-3)2 - 4(2)(k) = 9 - 8k

D = 0 gives us a double root.

9 - 8k = 0 add 8k to both sides
9 = 8k divide by 8 to both sides
9/8 = k

Thus for k = 9/8 we have a double root, which is x = -b/2a. So that x = -(-3)/2(2) = 3/4.