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Learn how to find the roots of a quadratic equation using different methods such as factoring, quadratic formula, completing the square, and graphing. See the definition, nature, sum, product, and discriminant of the roots with examples and practice problems.
We shall learn how to find the roots of quadratic equations algebraically and using the quadratic formula. The general form of a quadratic equation is ax 2 + bx + c = 0, where x is the unknown and a, b and c are known quantities such that a ≠ 0.
- The roots of a quadratic equation are those values of the unknown for the equation is equal to zero.
- A quadratic equation has 2 roots, they may be equal or distinct.
- The roots of a quadratic equation may be determined by factorising the given equation and by using the quadratic formula.
- If the given quadratic equation has real roots then the value of the discriminant D ≥ 0.
- If the value of the discriminant D = 0 then the quadratic equation has real roots.
May 28, 2024 · Learn how to find the roots or zeros of a quadratic equation using different methods such as quadratic formula, factoring, completing the square and graphical method. See examples, nature of roots, sum and product of roots and practice problems.
- 6 min
Learn how to determine the nature of roots of a quadratic equation based on the discriminant D = b2 – 4ac. Find real and complex roots using factorization, quadratic formula and completing the square methods.
- 7 min
Learn how to find the roots of a quadratic equation using the quadratic formula, completing the squares, or factoring. Explore the nature of roots based on the discriminant value and the range of the quadratic expression.
Learn how to find the roots of a quadratic equation by substituting values and using the quadratic formula. See solved examples and worksheets on quadratic equations.
Learn how to use the quadratic formula to solve quadratic equations, and see how it relates to factoring and completing the square. The quadratic formula is x = − b ± b 2 − 4 a c 2 a, where a, b, and c are the coefficients of the equation.
