Question

If α and β are the zeroes of the polynomial ax^2 + bx + c, find the value of α^2 + β^2

Answer 1

Explanation:

α + β = -b/a

αβ = c/a

α² + β² = (α + β)² - 2αβ

`= ((-b)/(a))^(2)-2(c)/(a)\\\\= (b^(2))/(a^(2))-(2c)/(a)\\\\=(b^(2))/(a^(2))-(2c*a)/(a*a)\\\\=(b^(2)-2ca)/(a^(2))`