(A) Given that $a, b, c$ are integers,the coefficients of the quadratic equation $ax^2 + bx + c = 0$ are rational.If one root of a quadratic equation

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(A) Given that $a, b, c$ are integers,the coefficients of the quadratic equation $ax^2 + bx + c = 0$ are rational.If one root of a quadratic equation with rational coefficients is of the form $\alpha + \sqrt{\beta}$ (where $\sqrt{\beta}$ is an irrational surd),then the other root must be its conjugate,$\alpha - \sqrt{\beta}$.Here,one root is $3 + \sqrt{5}$.Therefore,the other root is $3 - \sqrt{5}$.

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

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Let one root of $ax^2 + bx + c = 0$,where $a, b, c$ are integers,be $3 + \sqrt{5}$. Then the other root is:

A
$3 - \sqrt{5}$
B
$3$
C
$\sqrt{5}$
D
None of these

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4-2.Quadratic Equations and Inequations

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Let one root of $ax^2 + bx + c = 0$,where $a, b, c$ are integers,be $3 + \sqrt{5}$. Then the other root is:

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