If p and q are non-zero real numbers and ^3+ ^3=-p, =q , then a quadratic equation whose roots are ^2 , ^2 is :

Step-by-step solution

Given ^3+ ^3=-p and =q Let ^2 and ^2 be the root of required quadratic equation. So, ^2 + ^2 = ^3+ ^3 = -p q and ^2 ^2 = =q Hence, required quadratic equation is aligned &x^2- ( -p q ) x+q=0 & x^2+ p q x+q=0 q x^2+p x+q^2=0 aligned