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Find the value of 'p' for which the quadratic equation $px(x - 2) + 6 = 0$ has two equal real roots.
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Sol. $px(x - 2) + 6 = 0 \Rightarrow px^2 – 2px + 6 = 0$
$a = p, b = -2p, c = 6$
Quadratic equation has equal roots, $\therefore D = 0$
$b^2-4ac = 0 \Rightarrow 4p^2-24p = 0$
$4p (p – 6) = 0$
$p = 0, p = 6$
$p = 0$ rejected $\therefore p = 6$
$a = p, b = -2p, c = 6$
Quadratic equation has equal roots, $\therefore D = 0$
$b^2-4ac = 0 \Rightarrow 4p^2-24p = 0$
$4p (p – 6) = 0$
$p = 0, p = 6$
$p = 0$ rejected $\therefore p = 6$