# How do you find the discriminant and how many solutions does 9u^2-24u+16 have?

May 13, 2015

The equation is of the form color(blue)(au^2+bu+c=0 where:

$a = 9 , b = - 24 , c = 16$

The Discriminant is given by:

$\Delta = {b}^{2} - 4 \cdot a \cdot c$

$= {\left(- 24\right)}^{2} - \left(4 \cdot \left(9\right) \cdot 16\right)$

$= 576 - 576 = 0$

If $\Delta = 0$ then there is only one solution.
(for $\Delta > 0$ there are two solutions,
for $\Delta < 0$ there are no real solutions)

As $\Delta = 0$, this equation has ONE REAL SOLUTION

• Note :

The solutions are normally found using the formula
$u = \frac{- b \pm \sqrt{\Delta}}{2 \cdot a}$

As $\Delta = 0$, $u = \frac{- \left(- 24\right) \pm \sqrt{0}}{2 \cdot 9} = \frac{24}{18} = \frac{4}{3}$