$px^2+2x+3p = 0$ is the given quadratic equation and both roots are equal for this quadratic equation. Therefore, the discriminant of this quadratic equation is equal to zero.
If $ax^2+bx+c = 0$ is the quadratic equation and having equal roots, the discriminant $b^2-4ac$ is equal to zero.
$b^2 \,– 4ac = 0$
Compare the given quadratic equation with standard form quadratic equation. Therefore $a = p$, $b = 2$ and $c = 3p$ and substitute these values in the condition.
$\implies 2^2 \,–\, 4 \times p \times 3p = 0$
$\implies 4 \,–\, 12p^2 = 0$
$\implies 4 = 12p^2$
$\implies 12p^2 = 4$
$\implies p^2 = \dfrac{4}{12}$
$\require{cancel} \implies p^2 = \dfrac{\cancel{4}}{\cancel{12}}$
$\implies p^2 = \dfrac{1}{3}$
$\implies p = \pm \sqrt{\dfrac{1}{3}}$
$\therefore \,\, p = \pm \dfrac{1}{\sqrt{3}}$
The values of $p$ are $\dfrac{1}{\sqrt{3}}$ and $-\dfrac{1}{\sqrt{3}}$.
Learn how to solve easy to difficult mathematics problems of all topics in various methods with step by step process and also maths questions for practising.