The quadratic 2x^2 - 3x + 29 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.
2x^2 - 3x + 29 divide through by 2
x^2 - 3/2x + 29/2 roots r and s SUM to -3/2 and multiply to 29/2
(r+s)^2 = r^2 + s^2 + 2rs sub in the values above
(-3/2)^2 = r^2 + s^2 + 2 ( 29/2)
r^2 + s^2 = (-3/2)^2 - 2 ( 29/2) You can finish !