The quadratic equation 3 x^2- (k^2+5 k ) x+3 k^2-5 k=0 has real roots of equal magnitude and opposite sign. Which one of the following is correct?

Step-by-step solution

If the roots of a x^2+b x+c=0 are equal in magnitude but opposite in sign then a 0, b=0 and c 0 . k^2+5 k=0 k=0,-5 ....(i) aligned & 3 k^2-5 k 0 & k(3 k-5) 0 aligned 0 k 5 3 ....(ii) So, no any value of k which satisfied (i) and (ii).