A) Discriminant = 12
B) 2 Solutions
C) Real roots
D) Irrational solutions
Step-by-step explanation:
Given:
[tex]x^2+ 8x = 13[/tex]
A) Discriminant:
The discriminant of the quadratic equation following [tex]ax^2+bx+c=0[/tex] is equal to [tex]b^2 -4ac[/tex]. The notation used for the discriminant is Δ (delta), so we have [tex]\Delta =b^2 -4ac.[/tex]
[tex]x^2+ 8x = 13[/tex]
[tex]x^2+ 8x - 13 = 0[/tex]
Now the Discriminant
[tex]= (8)^2 - 4(1)(13)[/tex]
= 64 - 52
= 12
Thus [tex]\Delta =[/tex] 12
B. Number of solutions for the quadratic equation
The Given equation is quadratic equation. The quadratic equation has a degree two. when the calculation of the discriminant is a positive number, the equation has two distinct roots.So the number of solutions is 2
C. Type of solutions (circle one):
A positive discriminant indicates that the quadratic has two distinct real number solutions.
Hence the roots are real
D. Type of solutions
The discriminant is Real but they are not perfect squares . hence the Solutions are irrational
