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Solve Quadratic Equation: x² + 3x + 4 = 0
Published on August 5, 2024
Algebra
This math problem asks to determine the number of real roots for the quadratic equation x² + 3x + 4 = 0. Using the discriminant, we find that the equation has no real roots.
Question
How many real roots does the equation have?
Answer
To find the number of real roots of the quadratic equation
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
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