Question

(20 points) How many, and what type of solutions do the follow

quadratic equations have?
4x2 - x +4= 0

Answer 1

2 , Real

Explanation:

The quadratic equation is ,

⇒ 4x² - x - 4 = 0 .

Since it is a quadratic equation and has the highest degree of variable as 2 therefore it will have two solutions . For determining the nature of roots we will find the discriminant . The Discriminant of a quadratic equation in standard form of ax² + bx + c = 0 , is ,

⇒ D = b² - 4ac

⇒ D = (-1)² - 4 × 4 × (-4)

⇒ D = 1 + 64

⇒ D = 65 .

Since Discriminant is Greater than 0 , therefore the roots will be real .