If α and β are the roots of the polynomial ax2 + bx + c, then find the value of α2 + β2.

 Solution:-

Let p(x)=ax^2 + bx + c

and α + β = -b/a

 α β=c/a

then  α^2 + β^2= (α + β)^2 -  α β ......................(1)

put value of α + β = -b/a  and  α β=c/a in (1)

we get,

=(-b/a)^2 - 2 × c/a

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

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

 

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