# How do you use the discriminant to determine the nature of the solutions given  –4p^2 – 1.8p + 0.2 = 0?

Jan 14, 2017

The solutions are $= \left\{- 0.54 , 0.09\right\}$

#### Explanation:

We compare this equation to

$a {x}^{2} + b x + c = 0$

$- 4 {p}^{2} - 1.8 p + 0.2 = 0$

The discriminant is

$\Delta = {b}^{2} - 4 a c = {\left(- 1.8\right)}^{2} - 4 \cdot \left(- 4\right) \cdot \left(0.2\right)$

$= 3.24 + 3.2 = 6.44$

As $\Delta > 0$, we have 2 real roots

${p}_{1} = \frac{1.8 + \sqrt{6.44}}{2 \cdot - 4} = \frac{1.8 + 2.54}{-} 8 = - 0.54$

${p}_{2} = \frac{1.8 - \sqrt{6.44}}{2 \cdot - 4} = \frac{1.8 - 2.54}{-} 8 = 0.09$