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For a given quadratic equation ax 2 + bx + c = 0, the values of x that satisfy the equation are known as its roots. i.e., they are the values of the variable (x) which satisfies the equation. The roots of a quadratic function are the x-coordinates of the x-intercepts of the function.
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.
We use the quadratic formula to find the roots of a quadratic equation. The formula is given as \(\begin{array}{l}x = \frac{-b \pm \sqrt{b^2-4ac}}{2a}\end{array} \)
The formula to find the roots of the quadratic equation is x = [-b ± √(b 2 - 4ac)]/2a. The sum of the roots of a quadratic equation is α + β = -b/a. The product of the Root of the quadratic equation is αβ = c/a. The quadratic equation whose roots are α, β, is x 2 - (α + β)x + αβ = 0.
Then the formula will help you find the roots of a quadratic equation, i.e. the values of x where this equation is solved. The quadratic formula. x = − b ± b 2 − 4 a c 2 a. It may look a little scary, but you’ll get used to it quickly! Practice using the formula now. Worked example.
Feb 14, 2022 · The solutions to a quadratic equation of the form \(a x^{2}+b x+c=0, a \neq 0\) are given by the formula: \(x=\dfrac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}\) How to solve a quadratic equation using the Quadratic Formula. Write the quadratic equation in standard form, \(a x^{2}+b x+c=0\). Identify the values of \(a, b, c\). Write the Quadratic Formula.
How To Solve Them? The " solutions " to the Quadratic Equation are where it is equal to zero. They are also called " roots ", or sometimes " zeros " There are usually 2 solutions (as shown in this graph). And there are a few different ways to find the solutions: We can Factor the Quadratic (find what to multiply to make the Quadratic Equation)
Oct 6, 2021 · The quadratic formula (Equation \ref{quad}) provides us with a means to solve all quadratic equations. Example \(\PageIndex{2}\): Solve using the quadratic formula: \(3 x^{2}+6 x-2=0\).
Dec 13, 2023 · A highly dependable method for solving quadratic equations is the quadratic formula, based on the coefficients and the constant term in the equation. See Example. The discriminant is used to indicate the nature of the roots that the quadratic equation will yield: real or complex, rational or irrational, and how many of each. See Example.
May 28, 2024 · Roots of Quadratic Equation. The roots of a quadratic equation, which is typically written as ax2 + 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.
