Without solving the following quadratic equation, find the value … - Vidyadip

Question

Without solving the following quadratic equation, find the value of ‘p’ for which the given equation has real and equal roots:
$x^2 + (p – 3) x + p = 0$

✓

Answer

$x^2 + (p – 3) x + p = 0$
Here $a = 1, b = p - 3, c = p$
For real and equal roots
$D = b^2 - 4ac = 0$
$(p - 3)^2 - 4 \times 1 \times p = 0$
$p^2 - 6p + 9 - 4p = 0$
$p^2 - 10p + 9 = 0$
$\Rightarrow p^2 - p - 9 (p - 1) = 0$
$p(p - 1) - 9 (p - 1) = 0$
$\Rightarrow (p - 1) (p - 9) = 0$
$\Rightarrow p = 1$ or $p = + 9$

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