(A) Given the quadratic equation $x^2 + px + q = 0$ with rational coefficients,if one root is $2 + \sqrt{3}$,the other root must be its conjugate,$2 -

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(A) Given the quadratic equation $x^2 + px + q = 0$ with rational coefficients,if one root is $2 + \sqrt{3}$,the other root must be its conjugate,$2 - \sqrt{3}$.Sum of roots $= -p = (2 + \sqrt{3}) + (2 - \sqrt{3}) = 4$,which implies $p = -4$.Product of roots $= q = (2 + \sqrt{3})(2 - \sqrt{3}) = 2^2 - (\sqrt{3})^2 = 4 - 3 = 1$.Therefore,the values are $(p, q) = (-4, 1)$.

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

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If one root of the equation $x^2 + px + q = 0$ is $2 + \sqrt{3}$,then the values of $p$ and $q$ are:

A
$-4, 1$
B
$4, -1$
C
$2, \sqrt{3}$
D
$-2, -\sqrt{3}$

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4-2.Quadratic Equations and Inequations

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If one root of the equation $x^2 + px + q = 0$ is $2 + \sqrt{3}$,then the values of $p$ and $q$ are:

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