# How do you use the discriminant to determine the nature of the solutions given y = 9x + 3 – 5x^2?

Aug 19, 2017

Solution: $x \approx 2.087 , x \approx - 0.287$

#### Explanation:

$y = - 5 {x}^{2} + 9 x + 3$ . Comparing with standard quadratic equation

$a {x}^{2} + b x + c = 0$ here $a = - 5 , b = 9 , c = 3$. We know

discriminant of a quadratic equation is $D = {b}^{2} - 4 a c$

$= {9}^{2} - 4 \cdot \left(- 5\right) \cdot 3 = 141$ ,here discriminant is positive,

so we will get two real solutions.

The solutions can be calculated by using quadratic formula.

$x = \frac{- b \pm \sqrt{D}}{2 a} = \frac{- 9 \pm \sqrt{141}}{-} 10 = 0.9 \pm 1.187$ or

$x \approx 2.087 , x = - 0.287$ [Ans]