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

Discriminant is -4.

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

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 .

Answer 2

solutions are imaginary

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