Question

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

Answer 1

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

Answer 2

Here is your answer mate .