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Formula for sum and products of roots of quadratic equation with several examples, practice problems and diagrams.
Sum of Roots. Thus, the sum of roots of a quadratic equation is given by the negative ratio of coefficient of. \ (\begin {array} {l}x\end {array} \) and. \ (\begin {array} {l}x^2\end {array} \) The product of roots is given by ratio of the constant term and the coefficient of.
We see where the sum and product of the roots of quadratic equations (alpha and beta) can be used to solve problems.
To solve any quadratic equation, convert it into standard form ax 2 + bx + c = 0, find the values of a, b, and c, substitute them in the roots of quadratic equation formula and simplify. How to Find the Sum and Product of Roots of Quadratic Equation?
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.
The sum of the roots is (5 + √2) + (5 − √2) = 10. The product of the roots is (5 + √2) (5 − √2) = 25 − 2 = 23. And we want an equation like: ax2 + bx + c = 0. When a=1 we can work out that: Sum of the roots = −b/a = -b. Product of the roots = c/a = c. Which gives us this result.
The sum of roots x1 + x2 and the product of roots x1·x2 are common to problems involving quadratic equation.
