Question

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Answer 1

Answer: -5 , 7

Step-by-step explanation:

x⁴ - 6x³ - 26x² + 138x - 35

Given that (2 + √3),(2 - √3) are 2 zeroes of the expression

Since (2 + √3) is a zero , x - (2 + √3) is a factor of the polynomial .

Similarly since (2 - √3) is a zero , x - (2 - √3) is a factor of the polynomial .

So (x - 2 -  √3)(x - 2 + √3)

=> (x - 2)² - (√3)²                     [since (a + b)(a - b) = a² - b²]

=> x² - 4x + 4 - 3

=> x² - 4x + 1

So we divide (x² - 4x + 1) from (x⁴ - 6x³ - 26x² + 138x - 35)

For this check the attachment .

So we get (x² - 2x - 35) as the Quotient .

Factorise it , we get :-

x² - 7x + 5x - 35

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

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

So (x + 5) and (x - 7) are the other zeroes of the polynomial .

Or x = -5,7 are the other zeroes of the polynomial .

Hope this helps you .

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