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

May 19, 2018

$a$ must equal $- 2 \mathmr{and} 2$.

#### Explanation:

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

$\text{discriminant} = {b}^{2} - 4 a c$
It is modelled after the quadratic form $a {x}^{x} + b x + c$.

• 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 $c = 1$.

${a}^{2} - 4 \left(1\right) \left(1\right) = 0$

${a}^{2} - 4 = 0$

${a}^{2} = 4$

$a = - 2 \mathmr{and} 2$