The quadratic 2x^2 - 3x + 21 has two imaginary roots. What is the sum of the squares of these roots? Express your answer as a decimal rounded to the nearest hundredth.
+129850 2x^2 -3x + 21
Call the roots r and s
Sum of the roots = 3/2
r + s = 3/2
Square both sides
r^2 + 2rs + s^2 = 9/4 (1)
Product of the roots = rs
rs = 21/2
2rs = 21 (2)
Sub (2) into (1)
r^2 + 21 + s^2 = 9/4
r^2 + s^2 = 9/4 - 21
r^2 + s^2 = 9/4 - 84/4
r^2 + s^2 = - 75 / 4 = -18.75
