p=124,root(3)(p(p^(2)+3p+3)+1)=?

If P = 124, then root(3)(P(P^(2)+3P+3)+1)=?

If P=999 , then root(3)(P(P^(2)+3P+3)+1)=

p_(1)p_(2)p_(3)=

If p is a constant and f(x) =|(x^2,x^3,x^4),(2,3,6),(p,p^2,p^3)| if f'(x)=0 have roots alpha,beta , then (1) alpha and beta have opposite sign and equal magnitude at p= root (3) (2) At p=1 , f''(x)=0 represent an identity (3) at p=2 ,product of roots are unity (4) at p=- (root 3) product of roots are positive

Find the value of 'p' for which the qudratic equations have equal roots: (3p +1) c^(2) + 2 ( p+1) c+ p=0.

If each pair of the three equations x^(2) - p_(1)x + q_(1) =0, x^(2) -p_(2)c + q_(2)=0, x^(2)-p_(3)x + q_(3)=0 have common root, prove that, p_(1)^(2)+ p_(2)^(2) + p_(3)^(2) + 4(q_(1)+q_(2)+q_(3)) =2(p_(2)p_(3) + p_(3)p_(1) + p_(1)p_(2))

If each pair ofthe following three equations x: x^(2)+p_(1)x+q_(1)=0.x^(2)+p_(2)x+q_(2)=0x^(2)+p_(3)x+q_(3)=0, has exactly one root common, prove that (p_(1)+p_(2)+p_(3))^(2)=4(p_(1)p_(2)+p_(2)p_(3)+p_(3)p_(1)-q_(1)-q_(2)-q_(3)]