# How do you find the nature of the roots using the discriminant given 4x^2 + x + 5 = 0?

Jan 29, 2018

Nature of roots are complex and $x \approx - 0.125 \pm 1.11 i$

#### Explanation:

$4 {x}^{2} + x + 5 = 0$

Comparing with standard quadratic equation $a {x}^{2} + b x + c = 0$

$a = 4 , b = 1 , c = 5$ Discriminant $D = {b}^{2} - 4 a c$ or

$D = 1 - 80 = - 79$ If discriminant 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 discriminant is negative , so it has

complex roots . Quadratic formula: $x = \frac{- b \pm \sqrt{D}}{2 a}$or

x= (-1+-sqrt (-79))/8 or x=-1/8+- sqrt(79i^2)/8 ; [i^2=-1]

or $x \approx - 0.125 \pm 1.11 i$

Nature of roots are complex and $x \approx - 0.125 \pm 1.11 i$ [Ans]