Question

For which value of `m` does the graph of `y=18x^2+mx+2` have exactly one `x`-intercept?

Answer 1

We will have exactly one intercept for `m=+-12`

Explanation:

As `y=18x^2+mx+2` will have two intercepts on `x`-axis given by

`18x^2+mx+2=0`

If the discriminant is zero the intercepts will coincide.

As the discriminant is `m^2-4xx2xx18=m^2-144`,

we will have exactly one intercept if `m^2-144=0` or `m=+-12`

i.e. for `y=18x^2-12x+2` and `y=18x^2+12x+2`

graph{18x^2-12x+2 [-3, 3, -2, 5]}

graph{18x^2+12x+2 [-5, 5, -2, 5]}