The value of $p$ for which quadratic equation $3x^2-px+5=0$ has equal roots.

Given: Quadratic equation $3x^2-px+5=0$ has equal roots.

To do: To find the value of $p$.

Solution:

Given quadratic equation: $3x^2-px+5=0$

$a_1=3,\ b=-p$ and $c=5$

For equal roots, $D=0$

$\Rightarrow b^2-4ac=0$

$\Rightarrow ( -p)^2-4\times 3\times5=0$

$\Rightarrow p^2-60=0$

$\Rightarrow p^2=60$

$\Rightarrow p=\pm\sqrt{60}$

$\Rightarrow p=\pm2\sqrt{15}$

Thus, $p=\pm2\sqrt{15}$ for equal roots.

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Updated on: 10-Oct-2022

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