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Q.
Number of values of ' $p$ ' for which the equation $\left(p^2-3 p+2\right) x^2-\left(p^2-5 p+4\right) x+p-p^2=0$ possess more than two roots, is:
Complex Numbers and Quadratic Equations
Solution:
For $\left(p^2-3 p+2\right) x^2-\left(p^2-5 p+4\right) x+p-p^2=0$ to be an identity
$p^2-3 p+2=0 \Rightarrow p=1,2 $....(1)
$p^2-5 p+4=0 \Rightarrow p=1,4 $.......(2)
$p-p^2=0 \Rightarrow p=0,1$......(3)
For (1), (2) & (3) to hold simultaneously $p=1$.