Question

The graph of the function y=x^2+ax+1 touches to the X-axis if and only if a=?

Answer 1

`a` must equal `-2 or 2`.

Explanation:

To complete this problem, we will use the discriminant . This provides information about the roots of an equation.

`"discriminant" = b^2-4ac`
It is modelled after the quadratic form `ax^x+bx+c`.

• If the discriminant is positive, the quadratic has two roots.
• If the discriminant is negative, the quadratic has no roots.
• If the discriminant is `0`, the quadratic has `1` root.

In this example, we must use the last case, because we are looking for the point where the quadratic touches the `x`-axis once.

We know that, in this problem, `a=1`, `b=a`, and `c=1`.

`a^2-4(1)(1)=0`

`a^2-4=0`

`a^2=4`

`a=-2 or 2`