Let p, q(p q) be the roots of the quadratic equation x^2+b x+c=0 where c 0 . If p^2+q^2-11 p q=0 , then what is p-q equal to?

Step-by-step solution

Given that roots of x^2+b x+c=0 are p and q . p+q=-b and p q=c Given that aligned & p^2+q^2-11 p q=0 & (p+q)^2-13 p q=0 & b^2-13 c=0 aligned b^2-13 c ...(i) aligned & Now (p-q)^2=(p+q)^2-4 p q & =b^2-4 c=13 c-4 c=9 c & p-q=3 c aligned [from (i)]