Question

if alfa,beta are the zeroes of the polynomial ax2+bx+c, then (alfa2+beta2) = ?​

Answer 1

Answer :

$\boxed{\bf \alpha^2+ \beta^2=\frac{b^2-2ac}{a^2} }$

Step-by-step explanation :

=> α and β are the zeroes of the polynomial ax²+bx+c

=> α² + β² = ?

RELATIONSHIP BETWEEN ZEROES AND COEFFICIENTS :

=> Sum of zeroes = -(x coefficient)/x² coefficient

    α + β = -b/a

=> Product of zeroes = constant term/x² coefficient

        αβ = c/a

[ (a+b)² = a² + b² + 2ab ]

⇒ (α + β)² = α² + β² + 2αβ

    α² + β² = (α + β)² - 2αβ

    α² + β² = (-b/a)² - 2(c/a)

                $= \frac{b^2}{a^2} -\frac{2c}{a} \\\\ = \frac{b^2-2ac}{a^2}$