361,158 views
18 votes
18 votes
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

Determine the discriminant for the quadratic equation -3=x2+4x+1. Based on the discriminant-example-1
User Bonaldi
by
2.9k points

2 Answers

23 votes
23 votes

Answer:

1 aka b

Explanation:

User Matthew Shanley
by
3.0k points
12 votes
12 votes

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 = - 4ac

A quadratic equation a+ 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).

User Jesse Bunch
by
2.9k points