# How do you use the discriminant to determine the nature of the solutions given  –7q^2 + 8q + 2 = 0?

Sep 5, 2017

Two real solutions , $q \approx 1.35 \left(2 \mathrm{dp}\right) , q \approx - 0.21 \left(2 \mathrm{dp}\right)$

#### Explanation:

$- 7 {q}^{2} + 8 q + 2 = 0$ Comparing with standard quadratic equation

$a {x}^{2} + b x + c = 0$ , here $a = - 7 , b = 8 , c = 2 , D = b 2 - 4 a c$

$= {8}^{2} + 4 \cdot 7 \cdot 2 = 120$ is called the "discriminant". If $D$ is positive,

we get two real solutions, if it is zero we get just one solution, and

if it is negative we get complex solutions. Here $D$ is positive so

we will get two real solutions. $q = \frac{- b \pm \sqrt{D}}{2 a}$ or

$q = \frac{- 8 \pm \sqrt{120}}{- 14} \mathmr{and} q = \frac{4}{7} \pm \frac{\sqrt{30}}{7} \therefore q = \frac{1}{7} \left(4 \pm \sqrt{30}\right)$

or $q \approx 1.35 \left(2 \mathrm{dp}\right) , q \approx - 0.21 \left(2 \mathrm{dp}\right)$ [Ans]