Question

PLS ANSWER IT PLS If alpha and Beta are the zeroes of polynomial P(x) = 3x^2 + 2x + 1, find the polynomial whose zeroes are
1-alpha/1+alpha
and
1-beta/1+beta
​

Answer 1

Answer:

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Answer 2

Solution :-

[ A quadratic equation is a equation which has highest power of degree is 2 and it can be expressed in the form of ax^2 + bx + c = 0 ]

Here,

α and β are the Zeroes of the given equation 3x^2 + 2x + 1 .

If we compare 3x^2 + 2x + 1 with ax^2 + bx + c

Then,

a = 3 , b = 2 and c = 1

Now, We know that,

Sum of zeroes α + β = -b/a = -2/3

Product of zeroes αβ = c/a = 1/3

Now,

Sum of zeroes

1 - α / 1 + α + 1 - β / 1 + β

Take the LCM,

( 1 - α + β - αβ ) + ( 1 + α - β - αβ )/( 1 + α ) ( 1 + β )

= 2 - 2αβ/ 1 + α + β + αβ

Now put the values,

2 - 2/3 / 1 - 2/3 + 1/3

Therefore,

• The sum of zeroes = 4/3 / 2/3 = 2

Now,

The product of the zeroes

= ( 1 - α / 1 + α )( 1 - β / 1 + β )

= ( 1 - α ) ( 1 - β ) / ( 1 + α ) ( 1 + β )

= 1 - α - β + αβ / 1 + α + β + αβ

= 1 - ( α + β ) + αβ / 1 + ( α + β ) + αβ

Now, Put the required values

= 1 - 2/3 + 1/3 / 1 - 2/3 + 1/3

= 6/3 / 2/3

• Product of zeroes = 3$.$

Therefore,

The required polynomial will be

x2 - ( α + β )x + αβ

Put the required values,

= x^2 - 2x + 3