Question

Find the quadratic polynomial where zeros are 4&-2 ?

Answer 1

$\large \bf \clubs \:  Given :-$

For a Quadratic Polynomial :

   

• First Zero = 4

• Second Zero = -2

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$\large \bf \clubs \:   To  \: Find :-$

The Quadratic Polynomial.

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$\large \bf \clubs \:   Main  \:  Concept : -$

☆ If sum and product of zeros of any quadratic polynomial are S and P respectively,

Then,

The quadratic polynomial is given by :-

$\bf  {x}^{2}  - S \: x + P$

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$\large \bf \clubs \:  Solution  :-$

Here,

• Sum = S = 4 + (-2) = 2

• Product = P = 4 × (-2) = -8

So,

Required Polynomial should be :

$\bf  {x}^{2}  - S \: x + P$

$\large:\longmapsto \tt{x}^{2}  - 2x + (-8)$.

$\Large\purple{:\longmapsto\pmb{{x}^{2}  -2x -8}}$

$\Large \red{\mathfrak{  \text{W}hich \:   \: is  \:  \: the  \:  \: required} }\\ \huge \red{\mathfrak{ \text{ A}nswer.}}$

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Answer 2

EXPLANATION:-

GIVEN:-

2 Zeroes of a polynomial

TO FIND:-

The polynomial

STEP BY STEP EXPLANATION:-

If 4 and -2 are the zeroes of the polynomial ,

>x=4

>x-4=0

and

>x=-2

>x+2=0

So x-4 and x+2 are the factors  of the polynomial.So we know that polynomial is obtained by the product of it's factors.So let's find the product of it's factors.

(x+2)(x-4)

x(x-4)+2(x-4)        [Using distributive law]

x²-4x+2x-8

x²-2x-8                 [-4x+2x=-2x]

Hence the polynomial whose zeroes are 4 and -2 is x²-2x-8