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Enter coefficients for ax² + bx + c = 0
Understanding the foundation of quadratic equations
A quadratic equation is a second-degree polynomial equation in a single variable x, with a ≠ 0. The standard form of a quadratic equation is:
Where:
The quadratic formula provides the solution(s) to any quadratic equation. It is derived from completing the square of the standard quadratic equation:
The expression under the square root, b² - 4ac, is called the discriminant. It determines the nature of the roots:
Step-by-step guide to solving quadratic equations
From your quadratic equation in the form ax² + bx + c = 0, identify the values of a, b, and c.
Compute the value of the discriminant using the formula: D = b² - 4ac
Based on the discriminant value:
Substitute the values of a, b, and the discriminant into the quadratic formula:
Calculate the two possible values of x by using both the plus and minus signs in the formula.
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Find answers to common questions about quadratic equations
A quadratic equation is a second-degree polynomial equation in a single variable x, with the general form ax² + bx + c = 0, where a, b, and c are constants and a ≠ 0.
The quadratic formula is x = [-b ± √(b² - 4ac)] / 2a. It provides the solution(s) to any quadratic equation of the form ax² + bx + c = 0.
The discriminant (b² - 4ac) determines the nature of the roots:
Yes, when the discriminant equals zero, the quadratic equation has exactly one real solution (a repeated root).
If the discriminant is negative, the quadratic equation has two complex roots. Our calculator will display these complex solutions using the imaginary unit i (where i² = -1).
Absolutely! Our quadratic formula calculator is perfect for students to check their work, understand the solving process, and learn how to apply the quadratic formula correctly.
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