Question

if alpha and beta are the zeros of the polynomial 21 x square minus x minus 2 find a quadratic polynomial whose zeros are 2 alpha and 2 Beta​

Answer 1

Answer:

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 1/3 and

Beta be -2/7

✴ Now ,the new equation having Zeros as :-

2alpha and 2beta

Then , the Zeros are :-

2 alpha = 2×1/3 =2/3

2 beta = 2×-2/7 = -4/7

• Sum of the zeros ( of new equation )

2/3+(-4/7)

=14-12/21

=2/21

• Product of Zeros :-

2/3 ×(-4/7)

=-8/7

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

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

Putting value in the formula :-

x2 - 2/21x +(-8/21) = 0

21x^2 + 2x -8/21 = 0

21x² + 2x - 8 = 0

So, the required quadratic equation is :-

21x² + 2x - 8 = 0

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Answer 2

Step-by-step explanation:

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