If $2$ is the root of the quadratic equation $x^{2} + p^{2} x + 6 = 0$ , then the value of $(p i)^{2}$ (where $i = \sqrt{- 1}$ ) is

__

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Solution

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

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

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

$\Rightarrow 2 p^{2} = - 10$

$\Rightarrow p^{2} = - 5$

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

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If 2 is the root of the quadratic equation x2+p2x+6=0, then the value of (pi)2 (where i=√−1) is __

If 2 is the root, it should satisfy the quadratic equation. (2)2+p2(2)+6=0 ⇒4+2p2+6=0 ⇒2p2=−10 ⇒p2=−5 ⇒(pi)2=5

If $2$ is the root of the quadratic equation $x^{2} + p^{2} x + 6 = 0$ , then the value of $(p i)^{2}$ (where $i = \sqrt{- 1}$ ) is

__

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

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

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

$\Rightarrow 2 p^{2} = - 10$

$\Rightarrow p^{2} = - 5$

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