Question

If one root of $a{x}^2+bx+c=0$ where $a,b,c$ are integers be $3+\sqrt{5}$, then the other root is

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

Answer 1

The correct option is D

$3-\sqrt{5}$

If one root of a quadratic equation with rational coefficients is irrational and of the form α + $\sqrt{\beta }$, then the other root must also be irrational and of the form α - $\sqrt{\beta }$.

Here, if one root of $a{x}^2+bx+c=0$ where $a,b,c$ are integers be $3+\sqrt{5}$, then the other root is $3-\sqrt{5}$