# FORMATION OF QUADRATIC EQUATION WITH GIVEN ROOTS

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.

## Formation of quadratic equation with given 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 be the two roots of a quadratic equation are given , then the formula to form the quadratic equation is given by

x² - ( + )x + ᵦ  = 0

## Formation of quadratic equation with given roots - Examples

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

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

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)  =  2² - (√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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