Quadratic equation, product of roots

Question

It is given that one roots the quadratic equation x^2 + (p+3)x - p^2 = 0 , where p is a constant, is negative of the other. Find the value of the product of roots

Answer 1

suppose that r₁ & r₂ are the roots; then (x-r₁)(x-r₂) = 0 so x² -(r₁+r₂) +r₁r₂ = 0

 

Therefore c = -p² is the product of the two roots and b=-(p+3), using x² + bx + c = 0 as the quadratic equation.

 

If the two roots are OPPOSITES (which you have stated, albeit awkwardly), then b=0, so (p+3) = 0.

 

Therefore p must be -3 and therefore the product of the roots is -9.