If a root of the equation x^2 + px + 12 = 0 i | vedclass

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(C) Given that $4$ is a root of the equation $x^2 + px + 12 = 0$.Substituting $x = 4$ into the equation: $4^2 + p(4) + 12 = 0$.$16 + 4p + 12 = 0$ $\Ri

Vedclass · Accepted Answer

$49/4$

Vedclass · Answer

(C) Given that $4$ is a root of the equation $x^2 + px + 12 = 0$.Substituting $x = 4$ into the equation: $4^2 + p(4) + 12 = 0$.$16 + 4p + 12 = 0$ $\Rightarrow 4p = -28$ $\Rightarrow p = -7$.Now,the second equation is $x^2 + px + q = 0$,which becomes $x^2 - 7x + q = 0$.Since the roots of this equation are equal,the discriminant $D = b^2 - 4ac$ must be equal to $0$.$(-7)^2 - 4(1)(q) = 0$.$49 - 4q = 0$ $\Rightarrow 4q = 49$ $\Rightarrow q = \frac{49}{4}$.

If a root of the equation $x^2 + px + 12 = 0$ is $4$,while the roots of the equation $x^2 + px + q = 0$ are equal,then the value of $q$ will be:

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