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The roots of a quadratic equation are the values of the variable that satisfy the equation. They are also known as the "solutions" or "zeros" of the quadratic equation.
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.
Quadratic Equation in Standard Form: ax 2 + bx + c = 0; Quadratic Equations can be factored; Quadratic Formula: x = −b ± √(b 2 − 4ac) 2a; When the Discriminant (b 2 −4ac) is: positive, there are 2 real solutions; zero, there is one real solution; negative, there are 2 complex solutions
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.
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: α = − b + b 2 − 4 a c 2 a. β = − b − b 2 − 4 a c 2 a.
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
Not all quadratic equations are solved by immediately taking the square root. Sometimes we have to isolate the squared term before taking its root. For example, to solve the equation 2 x 2 + 3 = 131 we should first isolate x 2 .
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.
Feb 14, 2022 · If the equation fits the form \(a x^{2}=k\) or \(a(x-h)^{2}=k\), it can easily be solved by using the Square Root Property. Use the Quadratic Formula. Any other quadratic equation is best solved by using the Quadratic Formula.
We've seen linear and exponential functions, and now we're ready for quadratic functions. We'll explore how these functions and the parabolas they produce can be used to solve real-world problems.
