Question

. If α and β are zeros of x2

– x – 2, find a polynomial whose zeros are (2α + 1) and (2β + 1)​

Answer 1

Answer:

• x² - 4x - 5

Explanation:

Given polynomial,

⇒ x² - x - 2

Where α and β are the zeros.

We need to find the polynomial whose zeros are (2α + 1)(2β + 1)

Finding α and β of the given polynomial :-

⇒ x² - x - 2

⇒ x² + x - 2x - 2

⇒ x(x + 1) - 2(x + 1)

⇒ (x + 1)(x - 2)

⇒ x = -1 or, x = 2

Therefore, α = -1 and β = 2

Now, given zeros are (2α + 1) and (2β + 1)

• (2α + 1) = {2(-1) + 1} = -1
• (2β + 1) = {2(2) + 1} = 5

Sum of the zeros :-

⇒(2α + 1) + (2β + 1)

⇒ -1 + 5

⇒ 4

And also, product of zeros,

⇒ (2α + 1) × (2β + 1)

⇒ -1 × 5

⇒ -5

So the required polynomial is :-

⇒ x² - (sum of the zeros)x + product of the zeros

⇒ x² - (4)x + (-5)

⇒ x² - 4x - 5

_____________________

Answer 2

Answer:

okkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkk