If the roots of the equation x^2+p x+q=0 are in the same ratio as those of the equation x^2+l x+m=0 , then which one of the following is correct?

Step-by-step solution

Let a, b be the roots of x^2+p x+q=0 So, a + b =- p , ab = q ....(i) Let c , d be the roots of x ^2+ x + m =0 So, c + d =- , cd = m ....(ii) Given that roots of both the equations are in the Same ratio. So, a b = c d ....(iii) b a = d c ...(iv) aligned & (iii) + (iv) a b + b a = c d + d c & a ^2+ b ^2 ab = c ^2+ d ^2 ~cd a ^2+ b ^2 ab +2= c ^2+ d ^2 ~cd +2 & a ^2+ b ^2+2 ab ab = c ^2+ d ^2+2 ~cd ~cd & ( a + b )^2 ab = ( c + d )^2 ~cd & (- P )^2 q = (- )^2 ~m (from (i) and (ii)) & P ^2 ~m = ^2 q . aligned