To determine if the roots of the quadratic equation 5x² + 4x + 3 = 0 are real or non-real, we can use the discriminant (D). The discriminant is part of the quadratic formula used to find the roots of a quadratic equation:
The general form of a quadratic equation is:
ax² + bx + c = 0
In our case:
- a = 5
- b = 4
- c = 3
The discriminant is calculated using the formula:
D = b² – 4ac
Substituting the values of a, b, and c into the formula, we get:
D = (4)² – 4(5)(3)
D = 16 – 60
D = -44
Now, we analyze the discriminant:
- If D > 0, the roots are real and distinct.
- If D = 0, the roots are real and equal.
- If D < 0, the roots are non-real (complex).
Since our calculated discriminant is -44 (which is less than 0), the roots of the equation 5x² + 4x + 3 = 0 are non-real.