Question

Which of the following is a quadratic binomial ?

(i)(x + 2)(.1 - 1)
(ii) ( + 1)(x - 1)
(iii) (x +1)(x -2)
(iv) (r +2)(x + 1)​

Answer 1

Given : Expressions / polynomial

To Find : quadratic binomial  

(i)(x + 2)(.1 - 1)

(ii) ( + 1)(x - 1)

(iii) (x +1)(x -2)

(iv) (r +2)(x + 1)​

Solution:

(i)(x + 2)(.1 - 1)  

= (x + 2)(0)

= 0

(ii) ( + 1)(x - 1)

= x - 1

linear

(iii) (x +1)(x -2)

x² + x - 2x - 2

= x² -  x - 2

quadratic  

(iv) (r +2)(x + 1)​

rx + r + 2x + 2

linear

(x +1)(x -2)  is the correct answer

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Answer 2

SOLUTION

TO CHOOSE THE CORRECT OPTION

Which of the following is a quadratic binomial ?

(i)(x + 2)( x - 1)

(ii) ( x+ 1)(x - 1)

(iii) (x +1)(x -2)

(iv) (x +2)(x + 1)

CONCEPT TO BE IMPLEMENTED

POLYNOMIAL

Polynomial is a mathematical expression consisting of variables, constants that can be combined using mathematical operations addition, subtraction, multiplication and whole number exponentiation of variables

Degree of a polynomial

Degree of a polynomial is defined as the highest power of its variable that appears with nonzero coefficient

QUADRATIC BINOMIAL

A polynomial contains two Terms with highest power of its variable that appears with nonzero coefficient is 2 is called quadratic binomial

EVALUATION

CHECKING FOR OPTION : 1

Here the given polynomial is

$\sf{(x + 2)(x - 1)}$

We now simplify it as below

$\sf{(x + 2)(x - 1)}$

$\sf{ = {x}^{2} + 2x - x - 2 }$

$\sf{ = {x}^{2} + x - 2 }$

Since there are three terms ( Though highest power of its variable that appears with nonzero coefficient is 2 )

So it is not a quadratic binomial

CHECKING FOR OPTION : 2

Here the given polynomial is

$\sf{(x + 1)(x - 1)}$

$\sf{ = {x}^{2} - 1}$

Since there are two Terms and highest power of its variable x that appears with nonzero coefficient is 2

So it is a quadratic binomial

CHECKING FOR OPTION : 3

Here the given polynomial is

$\sf{(x + 1)(x - 2)}$

$\sf{ = {x}^{2} - 2x + x - 2 }$

$\sf{ = {x}^{2} - x - 2 }$

Since there are three terms ( Though highest power of its variable that appears with nonzero coefficient is 2 )

So it is not a quadratic binomial

CHECKING FOR OPTION : 3

Here the given polynomial is

$\sf{(x + 2)(x + 1)}$

$\sf{ = {x}^{2} + 2x + x + 2}$

$\sf{ = {x}^{2} + 3x + 2}$

Since there are three terms ( Though highest power of its variable that appears with nonzero coefficient is 2 )

So it is not a quadratic binomial

FINAL ANSWER

Hence the correct option is

$\sf{(ii) \: \: \: (x + 1)(x - 1)}$

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