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!
[tex]-3 = x^2 + 4x + 1[/tex]
[tex]0 = x^2 + 4x + 1 + 3[/tex]
[tex]\large { \boxed {x^2 + 4x + 4 = 0 } }[/tex]
Discriminant of the above quadratic equation could be calculated as shown below:
[tex]D = b^2 - 4 a c[/tex]
[tex]D = 4^2 - 4(1)(4)[/tex]
[tex]D = 16 - 16[/tex]
[tex]D = 0[/tex]
Because D = 0 → Equation has only one real number solution
Let us prove that :
[tex]-3 = x^2 + 4x + 1[/tex]
[tex]0 = x^2 + 4x + 1 + 3[/tex]
[tex]0 = x^2 + 4x + 4[/tex]
[tex]0 = x^2 + 2x + 2x + 4[/tex]
[tex]0 = x(x + 2) + 2(x + 2)[/tex]
[tex]0 = (x + 2)(x + 2)[/tex]
[tex]0 = (x + 2)^2[/tex]
[tex]x = -2[/tex]
The solution of the equation is x = -2
Learn more
- Solving Quadratic Equations by Factoring : https://brainly.com/question/12182022
- Determine the Discriminant : https://brainly.com/question/4600943
- Formula of Quadratic Equations : https://brainly.com/question/3776858
Answer details
Grade: High School
Subject: Mathematics
Chapter: Quadratic Equations
Keywords: Quadratic , Equation , Discriminant , Real , Number
