Question

Number of values of ' $p$ ' for which the equation $\left(p^2-3p+2\right)x^2-\left(p^2-5p+4\right)x+p-p^2=0$ possess more than two roots, is:

• A. 0
• B. 1
• C. 2
• D. 4

Answer 1

Answer: (B)

For $\left(p^2-3p+2\right)x^2-\left(p^2-5p+4\right)x+p-p^2=0$ to be an identity
$p^2-3p+2=0\Rightarrow p=1,2$....(1)
$p^2-5p+4=0\Rightarrow p=1,4$.......(2)
$p-p^2=0\Rightarrow p=0,1$......(3)
For (1), (2) & (3) to hold simultaneously $p=1$.