# Product of the roots formula explained with examples

Learn and know what is the product of the roots in quadratic equations chapter. Sum of roots and product of roots are two important formulas in quadratic equation.

Do you know what is the meaning of “roots” in Q.E? It is a value of the variable which is involved in the quadratic equation and which satisfies the quadratic equation is called as a root. Generally, quadratic equation will have “x” as variable and we call it as quadratic equation in “x”. Suppose if it is having “y” as variable then we call it as quadratic equation in “y”. Now we will learn meaning of quadratic equation and we will know how to find the product of roots.

## What is “quadratic equation” (Q.E) in math?

Generally, quadratic equation is defined as “an equation whose degree is equal to 2 is called as quadratic equation”. The general form Q.E is given as a${ x }^{ 2 }$ + bx + c = 0, where a, b and c are complex or real numbers and “a” is not equal to zero.

### What is mean by product of roots in Q.E?

For any given quadratic equation, there will be at most 2 roots. Multiplying the two roots and getting the result is nothing but product of roots. For this, we need to simplify the given quadratic equation and then we can find the product of the roots. Otherwise we can get in one more way i.e. by using formula.

#### How to find easily “product of the roots” in the Q.E?

To find the value of the product of the roots, there is a formula. Through this formula we can find easily the product of the roots.

The formula for the product of roots is “the ratio of constant term to the coefficient of ${ x }^{ 2 }$ in the quadratic equation” i.e. “$\frac { c }{ a }$”.

Examples:

${ x }^{ 2 }$ + 7x + 12 = 0 be a quadratic equation. Here, a value is 1, b value is 7 and c value is 12. The product of roots is given by $\frac { c }{ a }$ = $\frac { 12 }{ 1 }$ = 12.

Let us consider another quadratic equation. Let ${ x }^{ 2 }$ – 11x + 30 = 0. Here, a = 1, b = 11 and c = 30. The product of roots = $\frac { 30 }{ 1 }$ = 30.

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