Find the value of ' $p$ ' for which the given quadratic equation has equal roots $p k^{2} - 12 k + 9 = 0$

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Solution

Here, the given quadratic equation $p k^{2} - 12 k + 9 = 0$ is in the form $a x^{2} + b x + c = 0$ where $a = p, b = - 12$ and $c = 9$ .

It is given that the roots are equal, therefore $b^{2} - 4 a c = 0$ that is:

$b^{2} - 4 a c = 0 \Rightarrow (- 12)^{2} - (4 \times p \times 9) = 0$

$\Rightarrow 144 - 36 p = 0$

$\Rightarrow - 36 p = - 144$

$\Rightarrow 36 p = 144$

$\Rightarrow p = \frac{144}{36}$

$\Rightarrow p = 4$

Hence, $p = 4$

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Find the value of 'p' for which the given quadratic equation has equal roots pk2−12k+9=0

Here, the given quadratic equation pk2−12k+9=0 is in the form ax2+bx+c=0 where a=p,b=−12 and c=9. It is given that the roots are equal, therefore b2−4ac=0 that is:b2−4ac=0⇒(−12)2−(4×p×9)=0 ⇒144−36p=0⇒−36p=−144⇒36p=144⇒p=14436⇒p=4 Hence, p=4

Find the value of ' $p$ ' for which the given quadratic equation has equal roots $p k^{2} - 12 k + 9 = 0$