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:

36

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= 36

Answer to Q2

Two distinct solution and real

Explanation:

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.

Given equation is

x²-4x-5=0

x²-4x-5=0 has D=36 which is greater than zero.

hence, it has two distinct real solutions.

Answer 2

Answer: It has two distinct solutions and they are real.

Explanation:

1. By definition: if the discriminant is negative, the quadratic equation does not have real solutions, it has two imaginary solutions. If the discriminant is zero the quadratic has one solution. If the discriminant is positive, the quadratic equation has two distinct solutions.

2. The discriminant is:

`b^(2)-4ac=(-4)^(2)-4(1)(-5)=36`

3. The discriminant is positive, therefore, the quadratic equation has two distinct solutions and they are real.