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# Formula: Sum & Product of Roots

## Relationship between equation and roots

 Worksheet on this topic Sum and Product of Roots worksheet (free 25 question pdf with answer key) Quadratic Formula Calculator Quadratic Formula Home
The formulas

sum of roots: $$\frac{ -b}{a}$$

product of roots: $$\frac{ c}{a}$$

As you can see from the work below, when you are trying to solve a quadratic equations in the form of $$ax^2 +bx + c$$ . The sum and product of the roots can be rewritten using the two formulas above.
Example 1
The example below illustrates how this formula applies to the quadratic equation $$x^2 + 5x +6$$ . As you, can see the sum of the roots is indeed $$\color{Red}{ \frac{-b}{a}}$$ and the product of the roots is $$\color{Red}{\frac{c}{a}}$$ .

Example 2
The example below illustrates how this formula applies to the quadratic equation x2 - 2x - 8. Again, both formulas--for the sum and the product boil down to -b/a and c/a, respectively.

Practice Problems

Problem 1) Without solving, find the sum and product of the roots of the equation:
2x2 -3x -2 = 0

Problem 2) Without solving, find the sum & product of the roots of the following equation:
-9x2 -8x = 15