Let `p=cos(2 pi)/(7)+i sin(2 pi)/(7)` .The complex number `alpha=p+p^(2)+p^(4)``beta=p^(3)+p^(5)+p^(6)` is a root of the quadratic equation `x^(2)+ax+b=0`, where a and b are real

If (1-p) is a root of quadratic equation x^2+p x+(1-p)=0, then find its roots.

If (1-p) is a root of quadratic equation x^2+p x+(1-p)=0, then find its roots.

If p + iq be one of the roots of the equation x^(3) +ax +b=0 ,then 2p is one of the roots of the equation

If the sum of square of roots of equation x^2+(p+iq)x+3i=0 is 8, then find p and q, where p and q are real.

Find the values of p for whch the equadratic equation (2p+1)x^2-(7p+2)x+(7p-3)=0 has equal roots

If 2 is a root of the quadratic equation 3x^2+p x-8=0 and the quadratic equation 4x^2-2p x+k=0 has equal roots, find the value of kdot

If alpha, beta are the roots of the quadratic equation ax^(2) + bx + c = 0 then form the quadratic equation whose roots are palpha, pbeta where p is a real number.

Q. Let p and q real number such that p!= 0 , p^2!=q and p^2!=-q . if alpha and beta are non-zero complex number satisfying alpha+beta=-p and alpha^3+beta^3=q , then a quadratic equation having alpha/beta and beta/alpha as its roots is

Let p and q real number such that p!= 0 , p^3!=q and p^3!=-q . if alpha and beta are non-zero complex number satisfying alpha+beta=-p and alpha^3+beta^3=q , then a quadratic equation having alpha/beta and beta/alpha as its roots is

Let p, q, r in R and r gt p gt 0 . If the quadratic equation px^(2) + qx + r = 0 has two complex roots alpha and beta , then |alpha|+|beta| , is