Math, asked by rohit5757, 1 year ago

please answer correct​

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Answered by siddhartharao77
4

Answer:

-5,7

Step-by-step explanation:

Given p(x) = x⁴ - 6x³ - 26x² - 138x - 35.

Given zeroes are (2 + √3) and (2 - √3).

∴ [x - (2 + √3)][(x - (2 - √3)]

= (x - 2 - √3)(x - 2 + √3)

= (x - 2)² - (√3)²

= x² + 4 - 4x - 3

= x² - 4x + 1

So, x² - 4x + 1 is a factor of p(x).

Now,

We have to divide p(x) by x² - 4x + 1.

Long Division Method:

x² - 4x + 1) x⁴ - 6x³ - 26x² + 138x - 35 (x² - 2x - 35

                 x⁴ - 4x³ + x²

                 --------------------------------------

                        -2x³ - 27x² + 138x

                         -2x³ + 8x² - 2x

                    --------------------------------------

                                     -35x² + 140x - 35

                                      -35x² + 140x - 35

                     ------------------------------------------

                                                          0

Now,

We have to find other two zeroes of x² - 2x - 35.

= x² - 7x + 5x - 35

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

= (x + 5)(x - 7)

So, its zeroes are -5, 7.

Hence, all the zeroes of the polynomial are:

2 + √3, 2 - √3, -5,7

Hope it helps!

Answered by Anonymous
4

(x ± 2√3) are zeroes.

This means that (x-2-√3)(x-2+√3) are factors

(x - 2-√3)(x - 2+√3)

= (x - 2)^2 - (√3)^2

= x^2 - 4x +4 - 3

= x^2 - 4x + 1

x^2 - 4x + 1 is a factor of x^4 - 6x^3 - 26x^2 + 138x - 35.

Divide x^4 - 6x^3- 26x^2 + 138x - 35 with x^2- 4x+1

we get the answer as :-

x^2 - 2x - 35

x^2 - 7x + 5x - 35

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

(x + 5)(x - 7)

The other zeroes are :-

-5 and 7

Hope it help you

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