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.
+30 Call the roots m and n
By Vieta's Theorem......
ax^2 + bc + c
Sum of roots = m + n = -b/a = 3/2 square both sides m^2 + 2mn + n^2 = 9/4 (1)
Product of roots = mn = c/a = 27/2 and 2mn = 27 (2)
So......subbing (2) into ( 1) we have
m^2 + 27 + n^2 = 9/4
m^2 + n^2 = 9/4 - 27
m^2 + n^2 = [9 - 108 ] / 4 = - 99 / 4
