Question

If two zeroes of the polynomial x4- 6x^3- 26x^2 + 138x -35 are 2+√3, find the other zeroes.

Answer 1

Answer:

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Step-by-step explanation:

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Answer 2

Answer:

$\bold{• \: \: Zeros -> 7, -5}$

Step-by-step explanation:

Given :

Two zeroes of polynomial

• 2+√3
• 2-√3

To Find :

The other zero of polynomial

Solution :

$\bold{ {x}^{4} - {6x}^{3} - {26x}^{2} + 138x - 35}$

[x - (2 + √3)] [x - (2 - √3)]

= [x - 2 - √3] [x - 2 + √3]

= [(x - 2) - √3] [(x - 2) + √3]

= x² - 4 - 4x - 3

= x² - 4x + 1 is a factor of p(x)

Now, dividing the factor by the polynomial

We get x² - 2x - 35

Now,

x² - 2x - 35

= x² - 7x + 5x - 35

= x(x - 7) + 5(x - 7)

= (x - 7) (x - 5)

$\boxed{\pink{Zeroes \: \: are \: \: 7 \: and -5}}$