Math, asked by Rishabh5344, 1 year ago

If alpha and beta are the zeros of polynomial 21^-x-2 find the quadratic polynomial whose zeros are 2alpha and 2 beta

Answers

Answered by ALTAF11
66
Hi Mate !!


Here's ur ans :-


Given equation :- 21x² - x - 2

Let's factorise the equation by middle term splitting :0


21x² - x - 2 = 0

21x² - 7x + 6x - 2 = 0

7x ( 3x - 1 ) + 2 ( 3x - 1 ) = 0

( 3x - 1 ) ( 7x + 2 ) = 0

• ( 3x - 1 ) = 0

x = 1/3


• ( 7x + 2 ) = 0

x = - ( 2/7 )

 = )let \:  \alpha  \: be \:  \frac{1}{3 \: }  \: and \:  \beta  \: be \:  \frac{ - 2}{7}


✴ Now ,the new equation having Zeros as :-
2 \alpha  \: and \: 2 \beta

Then , the Zeros are :-

2 \alpha  = 2 \times  \frac{1}{3}  \\  =  \frac{2}{3}


2 \beta  = 2 \times  \frac{ - 2}{7}  =  \frac{ - 4}{7}

• Sum of the zeros ( of new equation )

 \frac{2}{3}  + ( \frac{ - 4}{7} )


 =  \frac{14 - 12}{21}


 =  \frac{2}{21}


• Product of Zeros :-

 \frac{2}{3}  \times ( \frac{ - 4}{7} )



 =  \frac{ - 8}{21}


♯ To form the quadratic equation we have formula as :-

x² - ( Sum of Zeros )x +(Product of Zeros )


Putting value in the formula :-


 {x}^{2}  -  \frac{2}{21} x + ( \frac{ - 8}{21} ) = 0


 \frac{21 {x}^{2}  + 2x - 8}{21}  = 0

21x² + 2x - 8 = 0


So, the required quadratic equation is :-
21x² + 2x - 8 = 0
Answered by khushi9944
33

Here is your answer mate .

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