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

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(A) Given that $4$ is a root of the equation $x^2 + px + 12 = 0$.Substituting $x = 4$ into the equation: $(4)^2 + p(4) + 12 = 0$.$16 + 4p + 12 = 0$.$4p + 28 = 0$.$4p = -28$.$p = -7$.Now,the second equation is $x^2 + px + q = 0$,which becomes $x^2 - 7x + q = 0$.Since this equation has equal roots,its discriminant $D = b^2 - 4ac$ must be $0$.Here,$a = 1$,$b = -7$,and $c = q$.$(-7)^2 - 4(1)(q) = 0$.$49 - 4q = 0$.$4q = 49$.$q = 49/4$.

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

Medium

If one root of the equation $x^2 + px + 12 = 0$ is $4$,and the equation $x^2 + px + q = 0$ has equal roots,then what is the value of $q$?

A
$49/4$
B
$4/49$
C
$4$
D
None of these

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4-2.Quadratic Equations and Inequations

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Solution of quadratic equations and Nature of roots

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If one root of the equation $x^2 + px + 12 = 0$ is $4$,and the equation $x^2 + px + q = 0$ has equal roots,then what is the value of $q$?

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