# How do you find all zeros of h(t)=t^2-6t+9?

Mar 5, 2018

3, that is the only root of $h \left(t\right)$.

#### Explanation:

$h \left(t\right)$ is a quadratic in $t$ which is :
$h \left(t\right) = {t}^{2} - 6 t + 9$
to find its zeros we equate the function with 0.
h(t) = 0 => t^2-6t+9 = 0

Now by splitting the middle term,
$\implies {t}^{2} - 3 t - 3 t + 9 = 0$
$\implies t \left(t - 3\right) - 3 \left(t - 3\right) = 0$
$\implies \left(t - 3\right) \left(t - 3\right) = 0$

Hence the root is 3.