+105 Find the sum of the squares of the roots of 3x^2 + 4x + 12 = 0.
thanks !
+129852 Call the roots a, b
The sum of the roots = -4/3
So
a + b = -4/3 square both sides of this
a^2 + 2ab + b^2 = 16/9 (1)
The product of the roots = 12/3 = 4
So
ab = 4
And
2ab =8 (2)
Sub (2) into (1) and we have that
a^2 + 8 + b^2 = 16/9
a^2 + b^2 = 16/9 - 8
a^2 + b^2 = 16/9 - 72/9
a^2 + b^2 = [ 16 - 72 ] / 9
a^2 + b^2 = -56 /9
