If p and q are the non-zero roots of the equation x^2+p x+q=0 , then how many possible values can q have?

Step-by-step solution

Since p and q are the non-zero roots of the equation aligned & x^2+p x+q=0 then & p^2+p^2+q=0 aligned q=2 p^2 .....(i) aligned & and q^2+p q+q=0 & q(q+p+1)=0 aligned q+p+1=0 [ q 0] -2 p^2+p+1=0 [ from(i) ] aligned & 2 p^2-p-1=0 & (p-1)(2 p+1)=0 & p=1, p =- 1 2 & q=-2,- 1 2 aligned