Question

alpha and beta are the zeros of the quadratic polynomial ax + bx+c find the value of (a) alpha^2+beta^2
b) alpha^2-beta^2​

Answer 1

Step-by-step explanation:

(a) alpha+beta = -b/a

= (alpha+beta)² = (-b/a)² (squaring both side)

=alpha²+beta²+2alpha×beta=b²/a²

=alpha²+beta²=b²/a²-2alpha×beta

as alpha×beta=c/a

alpha²+beta²=b²/a²-2c/a

=(b²-2ac)/a²

(b). alpha²+beta²-2alpha.beta

=(b²-2ac)/a²-2c/a

=(b²-2ac-2ac)/a²

=(b²-4ac)/a²

as alpha²+beta²-2alpha.beta=(alpha-beta)²

(b²-4ac)/a²=(alpha-beta)²

alpha-beta={(b²-4ac)/a²}^½

alpha-beta=(b²-4ac)^½/a

we have to find alpha²-beta²

alpha²-beta²=(alpha+beta)(alpha-beta)

=(-b/a){(b²-4ac)^½/a}

= {-b(b²-4ac)^½}/a

HOPE IT IS HELPFUL