Question

Determine the discriminant for the quadratic equation -3=x2+4x+1. Based on the

discriminant value, how many real number solutions does the equation have?
Discriminant = b2-4ac

Answer 1

1 aka b

Explanation:

Answer 2

Given -

x² + 4x + 1 = -3

To find -

the discriminant for the quadratic equation and to find how many real number solutions does the equation have. If it's discriminant = b² - 4ac

Concept applied -

As we know, Discriminant = b² - 4ac

A quadratic equation ax²+ bx + c = 0 has -

1. two distinct real roots, if b² - 4ac > 0 ,
2. two equal roots (i.e., coincident roots), if b²- 4ac = 0, and
3. no real roots, if b² - 4ac < 0.

Solution -

Solving the quadratic equation to bring it in the form of ax² + bx + c = 0,

➛ x² + 4x + 1 = -3

➛ x² + 4x +3 + 1 = 0

➛ x² + 4x + 4 = 0

Here,

a = 1, b = 4 and c = 4.

Putting the values in the the formula, b²- 4ac = 0.

➙ (4)²- 4(1)(4)

➙ 16- 16

➙ 0

As, b²- 4ac = 0 hence the quadratic equation will have two equal roots (i.e., coincident roots).