Both roots of $x^2+nx+144$ are equal to each other. Find all possible values of $n$ . Help?

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Answer 1 · 2017-12-18T08:08:57

The possible values of $n$ for which roots of $x^2+nx+144$ are equal are $-24$ and $24$ .

Roots of $x^2+nx+144$ are equal if discriminant $Delta=0$

Discriminant $Delta$ for a quadratic polynomial $ax^2+bx+c$ is $Delta=b^2-4ac$

Comparing $ax^2+bx+c$ and $x^2+nx+144$ , we have

$a=1$ , $b=n$ and $c=144$

and hence for roots of $x^2+nx+144$ to be equal, we should have

$n^2-4xx1xx144=0$

or $n^2-576=0$

or $(n-24)(n+24)=0$

i.e. $n=24$ and $n=-24$

Hence, the possible values of $n$ for which roots of $x^2+nx+144$ are equal are $-24$ and $24$ .

Both roots of x^2+nx+144x^2+nx+144 are equal to each other. Find all possible values of nn. Help?