Solve Quadratic Equation: x² + 3x + 4 = 0

Published on August 5, 2024

Question

How many real roots does the equation have?

Answer

To find the number of real roots of the quadratic equation , we can use the discriminant.
1. Recall the Discriminant
The discriminant, denoted as Δ (delta), is the part of the quadratic formula under the square root:
Δ = b² - 4ac
where a, b, and c are the coefficients of the quadratic equation ax² + bx + c = 0.
2. Calculate the Discriminant
In our equation, a = 1, b = 3, and c = 4. Let’s plug these values into the discriminant formula:
Δ = (3)² - 4 * 1 * 4
Δ = 9 - 16
Δ = -7
3. Interpret the Discriminant
  • If Δ > 0, the equation has two distinct real roots.
  • If Δ = 0, the equation has one real root (a double root).
  • If Δ < 0, the equation has no real roots (it has two complex roots).
Conclusion
Since the discriminant Δ is -7 (which is less than 0), the equation has no real roots.
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