Question

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

x^2 + 4x + 5 = 0

Answer 1

Answer to Q1:

-4

Explanation:

The formula to find discriminant is

D= b²-4ac

Given equation is

x²+4x+5=0

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

comparing given equation with general quadratic equation,we get

a= 1 ,b = 4 and c= 5

putting above values in the formula to find discriminant,we get

D= (4)²-4(1)(5)

D= 16-20

D= -4

Answer to Q2

Two solution and imaginary

Step-by-step explanation:

Given equation is

x²-4x-5=0

The formula to find discriminant is D= b²-4ac

If D < 0 , the quadratic equation has two imaginary solutions.

If D > 0, the quadratic equation has two distinct real solutions.

If D = 0 , the quadratic equation has one solution.

x²+4x+5=0 has D=-4 which is less than zero.

hence, it has two imaginary solutions.

Answer 2

D=-4<0, the equation has no real solutions, it has two imaginary solutions.

Explanation:

The quadratic equation
`x^2 +4x+5=0` has coefficients

a=1,

b=4,

c=5.

The discriminant D is the expression

`D=b^2-4ac.`

Hence,

`D=4^2-4\cdot 1\cdot 5=16-20=-4<0.`

Since the discriminant is negative, the equation has no real solutions, it has two imaginary solutions.