Let a and b be the roots of x^2 + (m - 2) x - (m + 3). Find a^2 + b^2.
The sum of the roots = (2 - m)
So
a + b = 2m square both sides of this
a^2 + 2ab + b^2 = 4m^2 (1)
The product of the roots = -( m + 3)
ab = -(m + 3)
2ab = -2(m + 3) (2)
Sub (2) into (1)
a^2 - 2 (m + 3) + b^2 = 4m^2
a^2 + b^2 = 4m^2 + 2(m + 3)
