Question

If alpha and beta are the zeroes of quadratic polynomial p (x)=x²-bx-c,then find the value of alpha²+beta².​

Answer 1

⇒If alpha,beta are roots of a quadratic equation ax^2+bx+c=0,then

alpha+beta=-b/a

alpha*beta=c/a

Therefore,alpha sq.+beta sq. =(alpha+beta)^2-2.alpha.beta

                                      =(-b/a)^2-2*c/a

                                      =b^2/a^2-2c/a

                                      =(b^2-2ac)/a^2

Answer 2

Answer:

Step-by-step explanation:

$alpha^2+beta^2=(alpha+beta)^2-2alphabeta\\=b^2-2(-c)\\=b^2+2c$