The quadratic 2x^2-3x+27+3x^2+5 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.
+1223 simplify the quadratic:
2x2−3x+27+3x2+5=5x2−3x+32
Let the roots be x and y. From Vieta's formulas, we know that:
sum of roots = x + y = 3/5
product of roots = xy = 32/5
sum of squares of roots = x^2 + y^2 = (x + y)^2 - 2xy = (3/5)^2 - 2(32/5) = -12.44
