**Formation of quadratic equation with given roots :**

Most if the student will know "How to solve a quadratic equation". But they may now know, how to construct a quadratic equation when two of its roots are given.

Here, we are going to see how to form a quadratic equation with the given two zeros or roots.

When two roots of a quadratic equation are given , the formula to form the quadratic equation is given by

**x² - (sum of the roots)x + product of the roots = 0 **

**If ****∝** and **ᵦ **be the two **roots of a quadratic equation are given , then the formula to form the quadratic equation is given by**

**x² - (****∝** + **ᵦ****)x + ****∝****ᵦ = 0**

**Example 1 : **

Form the quadratic equation whose roots are 2 and 3.

**Solution : **

Sum of the roots = 2 + 3 = 5

Product of the roots = 2 x 3 = 6

Formation of quadratic equation :

**x² - (sum of the roots)x + product of the roots = 0 **

**x² - 5x + 6 = 0 **

**Example 2 : **

Form the quadratic equation whose roots are 2/3 and 5/2.

**Solution : **

Sum of the roots = (2/3) + (5/2) = (4 + 15)/6 = 19/6

Product of the roots = (2/3) x (5/2) = 5/3

Formation of quadratic equation :

x² - (sum of the roots)x + product of the roots = 0

x² - (19/6)x + 5/3 = 0

(6x² - 19x + 10) / 3 = 0

**6x² - 19x + 10 = 0**

**Example 3 : **

If one root of a quadratic equation (2+√3), then form the equation given that the roots are irrational.

**Solution : **

Given : The two roots are irrational.

If the two roots of a quadratic equation are irrational, then the roots will occur in conjugate pairs.

If one root of a quadratic equation (2+√3), then the other root will be (2-√3).

Sum of the roots = 2+√3 + 2-√3 = 4

Product of the roots = (2+√3)(2-√3) = 2**² - (**√3)**²**

Product of the roots = 4** - **3

Product of the roots = 1

x² - (sum of the roots)x + product of the roots = 0

**x² - 4x + 1 = 0**

After having gone through the stuff given above, we hope that the students would have understood "Formation of quadratic- equation with given roots".

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