# Find a quadratic polynomial whose zeros are $3 \pm \sqrt 2 $ .

Answer

Verified

360.6k+ views

Hint: In such questions we should know how to express a quadratic polynomial in the form of the sum of its zeroes and product of its zeroes to reach the solution of the problem . Use the formula of ${a^2} - {b^2}$ = ( a+b )( a-b ) to simplify the calculation .

Complete step-by-step answer:

Given are the zeroes of the quadratic polynomial $3 + \sqrt 2 $ and $3 - \sqrt 2 $

We know that a quadratic polynomial = ${x^2}$ - ( sum of zeroes ) x + ( product of zeroes )

Sum of zeroes = $\left( {3 + \sqrt 2 } \right) + \left( {3 - \sqrt 2 } \right) = 6$

Product of zeroes = $\left( {3 + \sqrt 2 } \right)\left( {3 - \sqrt 2 } \right)$

$ = {3^2} - {\sqrt 2 ^2} = 9 - 2 = 7$

Hence the quadratic polynomial is ${x^2} - 6x + 4$ .

Note –

In such types of questions the key concept is to remember all the expressions of a quadratic polynomial along with the basic formulas used for calculation to get to the desired result in a faster and accurate way .

Complete step-by-step answer:

Given are the zeroes of the quadratic polynomial $3 + \sqrt 2 $ and $3 - \sqrt 2 $

We know that a quadratic polynomial = ${x^2}$ - ( sum of zeroes ) x + ( product of zeroes )

Sum of zeroes = $\left( {3 + \sqrt 2 } \right) + \left( {3 - \sqrt 2 } \right) = 6$

Product of zeroes = $\left( {3 + \sqrt 2 } \right)\left( {3 - \sqrt 2 } \right)$

$ = {3^2} - {\sqrt 2 ^2} = 9 - 2 = 7$

Hence the quadratic polynomial is ${x^2} - 6x + 4$ .

Note –

In such types of questions the key concept is to remember all the expressions of a quadratic polynomial along with the basic formulas used for calculation to get to the desired result in a faster and accurate way .

Last updated date: 25th Sep 2023

•

Total views: 360.6k

•

Views today: 4.60k

Recently Updated Pages

What do you mean by public facilities

Slogan on Noise Pollution

Paragraph on Friendship

Disadvantages of Advertising

Prepare a Pocket Guide on First Aid for your School

What is the Full Form of ILO, UNICEF and UNESCO

Trending doubts

How do you solve x2 11x + 28 0 using the quadratic class 10 maths CBSE

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Summary of the poem Where the Mind is Without Fear class 8 english CBSE

Difference Between Plant Cell and Animal Cell

What is the basic unit of classification class 11 biology CBSE

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

One cusec is equal to how many liters class 8 maths CBSE

Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE

Give 10 examples for herbs , shrubs , climbers , creepers