Find the discriminant of the quadratic equation then state the number and type of solution - Explain and Show Work

Question

-4a^2 - 5a - 1 = 0

Answer 1

-4x² - 5x - 1 = 0

 

a = -4

b = -5

c = -1

 

D = b² - 4ac = (-5)² - 4(-4)(-1) = 25 - 16 = 9

 

D > 0 ⇒ there are two distinct real roots

 

x = (-b ± √D) / (2a) = [-(-5) ± √9] / [2(-4)]

 

x = (5 ± 3) / (-8) = -1, -1/4

Answer 2

The discriminant is the name given to the expression that appears under the square root (radical) sign in the quadratic formula.

 

Quadratic Formula:

 

 

x=( -b+- sqrt b²-4ac) / 2a

 

Discriminant.

 b²-4ac

 

Here our equation is

 

-4a^2 - 5a - 1 = 0

 

a=-4

b=-5

c=-1

 

b²-4ac=(-5)²-4(-4)(-1)=25-4=21

 

The discriminant tells you about the "nature" of the roots of a quadratic equation given that a, b and c are rational numbers.

 

As b2-4ac >0

 

There are two real roots.