Question

Evaluate the discriminant of each equation. Tell how many solutions each equation has and whether the solutions are real or imaginary.

x^2 + 4x + 5 = 0

Answer 1

Answer:

solutions are imaginary

Step-by-step explanation:

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

Given equation is in the form of ax^2 + bx+c=0

a= 1 , b= 4  and c= 5

Discriminant is $b^2 - 4ac$

Plug in the values

D= $b^2 - 4ac$ = $4^2 - 4(1)(5)= -4$

Discriminant D = -4 that is negative

When Discriminant is negative then the solutions are imaginary

Answer 2

Answer:

Discriminant is -4.

x²+4x+5  = 0 have two imaginary solutions

Step-by-step explanation:

Given equation is :

x²+4x+5  = 0

ax²+bx+c  = 0 is general quadratic equation.

comparing given equation with quadratic equation,we get

a  = 1 ,b  = 4 and c  = 5

the formula to find discriminant is

D   = b²-4ac

putting above values in formula of discriminant,we get

D  = (4)²-4(1)(5)

D  = 16-20

D  = -4 < 0

The discriminant of given equation is not real hence, given equation have two imaginary solution .