Consider the following statements in respect to the quadratic equation 4(x-p)(x-q)-r^2=0 where p, q and r are real numbers : 1. The roots are real 2. The roots are equal if p=q and r=0 Which of the above statements is/are correct?

Step-by-step solution

aligned & 4(x-p)(x-q)-r^2=0 & =(x-p)(x-q)- r^2 4 =0 & =x^2-(p+q) x+p q- r^2 4 =0 aligned Discriminat, aligned & D =[-(p+q)]^2-4 (p q- r^2 4 )=0 & D =(p+q)^2-4 p q+r^2=0 & D =(p-q)^2+r^2=0 aligned We have D 0 real roots. and if p=q, r=0 the D =0 equal roots both statements are correct.