Question

If the sum of the squares of the zeros of the polynomial p(x)=x²+7x- ∆ is 25 find the value of ∆

Answer 1

let the roots be a and b
and we know (a^2)+(b^2) = (a+b)^2 -2ab
and a+b=-7. ,. and ab=-∆

therefore
25=(-7)^2 -2(-∆)
∆=-12

Answer 2

Let, roots be
$\alpha \: and \: \beta$
$\alpha + \beta = 25$
$\alpha \times \beta = - delta$
we know,
a²+b² =(a+b)²-2ab
and,a+b=-7 and ab=-delta
hence,
25=(-7)²-2(-delta)²
hence,
Delta=-12.