Answers to Matched Exercises in the tutorial of Solve Quadratic Equations Using Discriminants (1)

#### Matched Exercise 1:

Find all solutions to the quadratic equation given below.

x 2 - 3 x + 2 = 0

#### Answer to Matched Exercise 1:

The disriminant D = b
2 - 4 a c = (-3) 2 - 4 (1) (2) = 1. Since the discriminant is positive, the above equation has two real solutions
x
1 = (-b + √D) / (2 a) = (3 + 1) / 2 = 2
x
2 = (- b - √D) / (2 a) = (3 - 1) / 2 = 1

#### Matched Exercise 2.

Find all solutions to the quadratic equation.

x 2/2 = - 8 - 4x

#### Answer to Matched Exercise 2:

Multiply all terms in the above equation by 2 and write it in standard form.
x
2 + 8x + 16 = 0

The disriminant D = 0. Since the discriminant is equal to zero, the above equation one real solution.
x = - 4

#### Matched Exercise 3.

Find all solutions to the quadratic equation.

x 2 - 4x + 5 = 0

#### Answer to Matched Exercise 3:

The disriminant D = - 4. Since the discriminant is negative, the above equation has two imaginary solutions.
x = 2 + i
x = 2 - i
where i = √(-1) is the imaginary unit.

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