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.
Call the roots a, b
By Vieta
The sum ot the roots = a + b = (3/2)......square both sides ⇒ a^2 + 2ab + b^2 = 9/4 (1)
The product of the roots = ab = 29/2 ⇒ so 2ab = 29 (2)
Sub (2) into (1)
a^2 + 29 + b^2 = 9/4
a^2 + b^2 = 9/4 - 29
a^2 + b^2 = -107 / 4
