Question

if alpha and beta are the zeros of polynomial X square + 7 x + 12 then from a quadratic polynomial whose zeros are 2 alpha and 2 beta​

Answer 1

Answer:

The polynomial whose zeros are 2α and 2β is x² + 14x + 48

Explanation:

Given polynomial,

⇒ x² + 7x + 12

Whose zeros are α and β

We need to find the polynomial whose zeros are 2α and 2β

Let's calculate α and β :-

On factorising the polynomial,

⇒ x² + 3x + 4x + 12

⇒ x(x + 3) + 4(x + 3)

⇒ (x + 3) + (x + 4)

Then, zeros of the polynomial are -3 and -4

∴ α = -3 and β = -4

Now,

New zeros are :-

→ 2α

→ 2(-3)

→ -6

And also,

→ 2β

→ 2(-4)

→ -8

The required polynomial is given by,

→ x² - (sum of zeros)x + product of zeros

→ x² - [(-6) + (-8)]x + (-6)*(-8)

→ x² - [ - 6 - 8 ]x + 48

→ x² - [ -14]x + 48

→ x + 14x + 48

Required answer: x² + 14x + 48

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