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

Discriminant is 0, 1 real solution

Explanation:

Set the equation in form of
`\displaystyle \large{ax^2+bx+c=0}`:

`\displaystyle \large{x^2+4x+1+3=0}\\\\\displaystyle \large{x^2+4x+4=0}`

Apply discriminant formula which is
`\displaystyle \large{b^2-4ac}`:

`\displaystyle \large{D=4^2-4(1)(4)}\\\\\displaystyle \large{D=16-16}\\\\\displaystyle \large{D=0}`

Therefore, the discriminant is 0. Since D = 0, it’s defined that there are only 1 real solution.