Question

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

Answer 1

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

Explanation:

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`.