Question

Let one root of $a{x}^2+bx+c=0$ where $a,b,c\in Z,a\ne 0$ be $3+\sqrt{5}$, then the other root of the equation will be

• A. $\sqrt{5}$
• B. $3$
• C. $-3+\sqrt{5}$
• D. $3-\sqrt{5}$

Answer 1

The correct option is D $3-\sqrt{5}$

Given that one root of $a{x}^2+bx+c=0$ where $a,b,c$ are integers and $a\ne 0$ is $3+\sqrt{5}$.

If one root of a quadratic equation with rational coefficients is irrational and of the form $\alpha +\sqrt{\beta }$, then the other root must also be irrational and of the form $\alpha -\sqrt{\beta }$.
$\therefore$ The other root of the equation will be $3-\sqrt{5}.$