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Learn how to find the roots of a quadratic equation using the quadratic formula and other methods such as factoring, completing the square, and graphing. See examples, discriminant, nature of roots, and more.
Learn how to find the roots of a quadratic equation by completing the squares, splitting the middle term or using the quadratic formula. Also, learn how to determine the nature of the roots based on the discriminant.
- 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.
Aug 3, 2023 · The roots of a quadratic equation are the values of the variable that satisfies the equation. They are also known as the ‘zeroes’ of the quadratic equation. For the equation ax 2 + bx + c = 0 the two roots α and β are: $ {\alpha =\dfrac {-b+\sqrt {b^ {2}-4ac}} {2a}}$. β = $ {\dfrac {-b-\sqrt {b^ {2}-4ac}} {2a}}$.
May 28, 2024 · Roots of Quadratic Equation. The roots of a quadratic equation, which is typically written as ax 2 + bx + c = 0 where a, b, and c are constants and a ≠ 0. Roots of a Quadratic Equation are the values of the variable let’s say x for which the equation gets satisfied.
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Learn how to find the roots of a quadratic equation using the quadratic formula, which is derived by completing the square. Also, explore the nature of roots, formulas, and methods to solve quadratic equations.
Learn how to derive the quadratic formula, a closed-form expression for the solutions of a quadratic equation, using different methods such as completing the square, substitution, or Lagrange resolvents. See the geometric interpretation, equivalent formulations, and numerical calculation of the formula.
Learn the quadratic formula to find the roots of a quadratic equation and the nature of roots depending on the discriminant. See an example problem with solution and a video lesson on quadratic equations.
