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

Answer:

Step-by-step explanation:

α + β = -b/a

αβ = c/a

α² + β² = (α + β)² - 2αβ

           $= (\frac{-b}{a})^{2}-2\frac{c}{a}\\\\= \frac{b^{2}}{a^{2}}-\frac{2c}{a}\\\\=\frac{b^{2}}{a^{2}}-\frac{2c*a}{a*a}\\\\=\frac{b^{2}-2ca}{a^{2}}$