To determine whether the roots of the quadratic equation 5x² + 4x + 3 = 0 are real or non-real, we can use the discriminant. The discriminant, denoted as D, is given by the formula:
D = b² – 4ac
In our quadratic equation, the coefficients are:
- a = 5
- b = 4
- c = 3
Now, we can substitute the values of a, b, and c into the formula for the discriminant:
D = (4)² – 4(5)(3)
Calculating this gives us:
D = 16 – 60
D = -44
Since the discriminant is less than zero (D < 0), we conclude that the roots of the equation are non-real (complex). Therefore, the quadratic equation 5x² + 4x + 3 = 0 does not have real roots.