Question

A quadratic equation of the form ax^2+bx+ c=0 has positive coefficients ..if alpha and beta are the integral roots of the equation then find the value of alpha square +beta square +alpha.beta

Answer 1

A quadratic equation of the form ax^2+bx+ c=0 has positive coefficients ..if alpha and beta are the integral roots of the equation ..

so œ+ß=-b/a

→œß=c/a

now œ²+ß²+œß

→(œ+ß)²-2œß+œß

→(-b/a)²-c/a

→b²/a²-c/a

→(b²-ac)/a²

I hope this will help u :)

Answer 2

Hey there! ^_^

Praneeth from Brainly.in here to help!

➺ Given quadratic equation = ax²+bx+ c=0
➺ Roots are α,β

➺ Sum of the roots

=α+β

=-b/a

➺Product of roots

= αβ

=c/a

α²+β²+ αβ

=( α+ β)²-2αβ+ αβ

= ( α+ β)²- αβ

= (-b/a)²-c/a

=b²/a²-c/a

= (b²-ac)/a²

∴There fore, α²+β²+ αβ = (b²-ac) /a²

hope helped!