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


real number solutions

Answer 1

Based on the discriminant value, the equation has one real number solution

Further explanation

Discriminant of quadratic equation ( ax² + bx + c = 0 ) could be calculated by using :

D = b² - 4 a c

From the value of Discriminant , we know how many solutions the equation has by condition :

D < 0 → No Real Roots

D = 0 → One Real Root

D > 0 → Two Real Roots

Let us now tackle the problem!

$-3 = x^2 + 4x + 1$

$0 = x^2 + 4x + 1 + 3$

$\large { \boxed {x^2 + 4x + 4 = 0 } }$

Discriminant of the above quadratic equation could be calculated as shown below:

$D = b^2 - 4 a c$

$D = 4^2 - 4(1)(4)$

$D = 16 - 16$

$D = 0$

Because D = 0 → Equation has only one real number solution

Let us prove that :

$-3 = x^2 + 4x + 1$

$0 = x^2 + 4x + 1 + 3$

$0 = x^2 + 4x + 4$

$0 = x^2 + 2x + 2x + 4$

$0 = x(x + 2) + 2(x + 2)$

$0 = (x + 2)(x + 2)$

$0 = (x + 2)^2$

$x = -2$

The solution of the equation is x = -2

Learn more

• Solving Quadratic Equations by Factoring : brainly.com/question/12182022
• Determine the Discriminant : brainly.com/question/4600943
• Formula of Quadratic Equations : brainly.com/question/3776858

Answer details

Grade: High School

Subject: Mathematics

Chapter: Quadratic Equations

Keywords: Quadratic , Equation , Discriminant , Real , Number

Answer 2

-3 = x^2 + 4x + 1

0 = x^2 + 4x + 1 + 3

0 = x^2 + 4x + 4

Discriminant is b^2 - 4ac.

4^2 - 4(1)(4)

16 - 4(4)

16 - 16 = 0

Discriminant Rules:

1. If b²-4ac is negative, there are no real answers.
2. If b²-4ac is zero, there is one real answer.
3. If b²-4ac is positive, there are two real answers.

Based on rule 2, the answer is ONE REAL ROOT.