# Sum and product of roots pdf

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- SUM AND PRODUCT OF ROOTS OF QUADRATIC EQUATION WORKSHEET
- Sum and Product of Roots Worksheet
- Sum and Product of the Roots Worksheets
- Sum and Product of the Roots Worksheets

Now, let us evaluate the sum and product of roots of the equation we are looking for. We have:. You may observe that for this value of p , the roots of the equation are non-real. However, one root is the square of the other you can verify this if you know how to manipulate complex numbers.

## SUM AND PRODUCT OF ROOTS OF QUADRATIC EQUATION WORKSHEET

We have seen that the b 2 - 4 ac portion of the quadratic formula, called the discriminant , can tell us the type of roots of a quadratic equation.

The quadratic formula can also give us information about the relationship between the roots and the coefficient of the second term and the constant of the equation itself. Consider the following:. We can also see these relationships emerge from factoring the quadratic equation. The roots will be represented as r 1 and r 2. But, let's put our new formulas to use and apply the relationship between the roots and the coefficients and constants. See Creating Quadratic Equations to see why this may not be the only possible equation.

The sum of the roots of a quadratic equation is equal to the negation of the coefficient of the second term, divided by the leading coefficient. The product of the roots of a quadratic equation is equal to the constant term the third term , divided by the leading coefficient. You will discover in future courses, that these types of relationships also extend to equations of higher degrees. Yes, this question can be answered by simply multiplying the factors formed by these roots:. NOTE: The re-posting of materials in part or whole from this site to the Internet is copyright violation and is not considered "fair use" for educators.

Please read the " Terms of Use ". The sum of the roots is So the coefficient of the second term is. The product of the roots is.

## Sum and Product of Roots Worksheet

If a quadratic equation is given in standard form, we can find the sum and product of the roots using coefficient of x 2 , x and constant term. Let us consider the standard form of a quadratic equation,. Here a, b and c are real and rational numbers. Then the formula to get sum and product of the roots of a quadratic equation is,. Example 1 :. Find the sum and product of roots of the quadratic equation given below. First write the given quadratic equation in standard form.

The formula above, and other similar formulas shown below, still work in this case. We can find simple formulas for the sum and product of the roots simply by expanding out. From these formulas, we can also find the value of the sum of the squares of the roots of a quadratic without actually solving the quadratic. If the roots were real, then the sum of their squares would be positive. Note that, in the previous exercise, the desired expressions are symmetric. Such expressions are called symmetric functions of the roots. Thus, if a quadratic has two positive real solutions, we can express their arithmetic and geometric mean using the above formulas.

Problem 1 :. Find the sum and product of roots of the quadratic equation given below. If the product of roots of the quadratic equation given below is 4, then find the value of m. If the sum of roots of the quadratic equation given below is 0, then find the value of p. If the product of roots of the quadratic equation given below is 1, then find the value of m.

When the quadratic equation ax2 bx c 0 has roots and: ○ The sum of the roots, b a. ;. ○ and the product of roots, a.

## Sum and Product of the Roots Worksheets

We can expand the left side of the above equation to give us the following form for the quadratic formula:. Remembering the difference of squares formula, we have. Let's now go on to learn how the graph of a quadratic function is a parabola: 4. The Graph of the Quadratic Function.

We have seen that the b 2 - 4 ac portion of the quadratic formula, called the discriminant , can tell us the type of roots of a quadratic equation. The quadratic formula can also give us information about the relationship between the roots and the coefficient of the second term and the constant of the equation itself. Consider the following:. We can also see these relationships emerge from factoring the quadratic equation. The roots will be represented as r 1 and r 2.

Employ this ensemble of printable worksheets to help learners in high school identify the sum and product of the roots, find the missing root, forming quadratic equations with the given roots and much more. A few MCQ worksheets also have been incorporated here to gauge your understanding on the topic. A number of free worksheets are up for grabs! Use various download options available to access all worksheets under this topic that provides for ample practice.

### Sum and Product of the Roots Worksheets

In this article we cover quadratic equations — definitions, formats, solved problems and sample questions for practice. A quadratic equation is a polynomial whose highest power is the square of a variable x 2 , y 2 etc. For every quadratic equation, there can be one or more than one solution. These are called the roots of the quadratic equation. We have to take two numbers adding which we get 5 and multiplying which we get 6. They are 2 and 3. Let us verify that.

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Topic 7: Sum and Product of the Root. Sum & Product of the Roots – General. Recall: The ROOTS of an equation are what we get when the equation is set equal.

#### Solved examples of Quadratic equations

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