Question

If alpha and beta are two zeroes of f(x)=3x2+5x+2 find a quadratic polynomial whose zeroes are 2alpha/beta+2beta/alpha

Answer 1

Step-by-step explanation:

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Answer 2

Answer:

Given:

p(x) = 3x² + 5x - 2

α & β are the zeroes

To Find:

A polynomial with zeroes 3α + 2β and 2α + 3β

In p(x)

α + β = -b/a

α + β = -5/3

αβ = c/a

αβ = -2/3

Let the new polynomial g(x) = a'x² + b'x + c'

Zeroes of g(x) ⇒ 3α + 2β = α' & 2α + 3β = β'

α' + β' = -b'/a'

3α + 2β + 2α + 3β = -b'/a'

5(α + β) = 5(-5/3) = -b'/a'

-25/3 = -b'/a'

α'β' = c/a

(3α + 2β) x (2α + 3β) = c'/a'

6(α²+β²) +13αβ = c'/a'

6({α+β}² - 2αβ) + 13αβ = c'/a'

6(4/9 - 2(-2/3)) + 13(-2/3) = c'/a'

32/3 - 26/3 = c'/a'

6/3 = c'/a'

∴ The new polynomial is a'x² + b'x + c'

⇒3x² - 25x + 6

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