Question

solve the question above mentioned​

Answer 1

Step-by-step explanation:

Given -

α and β are zeroes of polynomial

p(x) = 4x² + 4x + 1

To Find -

A quadratic polynomial whose zeroes are 2α and 2β

Now,

» 4x² + 4x + 1

» 4x² + 2x + 2x + 1

» 2x(2x + 1) + 1(2x + 1)

» (2x + 1)(2x + 1)

Zeroes are -

» 2x + 1 = 0 and 2x + 1 = 0

• » x = -1/2 and x = -1/2

Now,

Let α = -1/2 and β = -1/2

Then,

2α = 2×-1/2 = -1

2β = 2×-1/2 = -1

New Zeroes -

• α = -1 and β = -1

Now,

• Sum of zeroes = -1 + (-1) = -1 - 1 = -2

And

• Product of zeroes = -1 × -1 = 1

As we know that :-

For a Quadratic polynomial :-

x² - (sum of zeroes)x + (product of zeroes)

It means,

» x² - (-2)x + (1)

» x² + 2x + 1

Hence,

The quadratic polynomial whose zeroes are 2α and 2β is x² + 2x + 1

Answer 2

Answer:

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Step-by-step explanation:

α and β are the zeroes of 4x² + 4x +1

a = 4

b =4

c = 1

sum of zeroes = -b/a

α + β = -b/a

α+ β = -4 /4

α + β = -1 ........................(i)

product of zeroes = c/a

αβ = c/a

αβ = 1/4 ................(ii)

zeroes of polynomial are 2α and 2β

so

sum of zeroes =

2α + 2 β

2(α+β) from (i)

2(-1)

-2

product of zeroes

(2α)(2β)

4αβ

4 (1/4) from (ii)

1

polynomial =

x ² - ( sum of zeroes )x + product of zeroes

x² - (-2)x +1

x² +2 x+1