Question

Form the quadratic equation whose roots are $3,5$

Answer 1

We know that if $m$ and $n$ are the roots of a quadratic equation $a{x}^2+bx+c=0$, then the sum of the roots is $(m+n)$ and the product of the roots is $\left(mn\right)$. And then the quadratic equation becomes $x^2-(m+n)x+mn=0$

Here, it is given that the roots of the quadratic equation are $m=3$ and $n=5$, therefore,

The sum of the roots is:

$m+n=3+5=8$

And the product of the roots is:

$m\times n=3\times 5=15$

Therefore, the required quadratic equation is

$x^2-(m+n)x+mn=0$

$\Rightarrow$$x^2-8x+15=0$

Hence, $x^2-8x+15=0$ is the quadratic equation whose roots are $3$ and $5$.