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Nature of Roots

If 2 is the r...

Question

If 2 is the root of the quadratic equation $x^{2} + p^{2} x + 6 = 0$ . Find the value of $(p i)^{2}$

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Solution

If 2 is the root it should satisfy the quadratic equation.

$(2)^{2} + p^{2} (2) + 6 = 0$

$4 + 2 p^{2} + 6 = 0$

$2 p^{2} = - 10$

$p^{2} = - 5$

$(p i)^{2} = 5$

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