(C) Given that $3$ is a root of the equation $x^2 + kx - 24 = 0$.Substituting $x = 3$ into the equation:$3^2 + k(3) - 24 = 0$$9 + 3k - 24 = 0$$3k - 15

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(C) Given that $3$ is a root of the equation $x^2 + kx - 24 = 0$.Substituting $x = 3$ into the equation:$3^2 + k(3) - 24 = 0$$9 + 3k - 24 = 0$$3k - 15 = 0$$3k = 15 \implies k = 5$.Now,check the options by substituting $x = 3$ and $k = 5$:For option $(C)$: $x^2 - kx + 6 = 0$Substituting $x = 3$ and $k = 5$:$3^2 - 5(3) + 6 = 9 - 15 + 6 = 0$.Since the equation is satisfied,$3$ is a root of $x^2 - kx + 6 = 0$.

Class 11 Mathematics 4-2.Quadratic Equations and Inequations Solution of quadratic equations and Nature of roots

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If $3$ is a root of the equation $x^2 + kx - 24 = 0$,then $3$ is also a root of which of the following equations?

A
$x^2 + 5x + k = 0$
B
$x^2 - 5x + k = 0$
C
$x^2 - kx + 6 = 0$
D
$x^2 + kx + 24 = 0$

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4-2.Quadratic Equations and Inequations

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If $3$ is a root of the equation $x^2 + kx - 24 = 0$,then $3$ is also a root of which of the following equations?

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