Find the set of values of $p$ for which the equation $p x^{2} - 5 x + p = 0$ has real and equal roots.

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Solution

For real and equal roots discriminant $= 0$
$D^{2} = b^{2} - 4 a c$
$D = 25 - 4 p^{2} = 0$
$p^{2}, \frac{25}{4}$
$p = \pm \frac{5}{2}$ .

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