Question

solve this question ​

Answer 1

According to the Question:-

➭ P(x) = x⁴ - 6x³ - 26x² + 138x - 35

➭ x = 2 + √3 , x = 2 - √3

➭ (x - 2 - √3). (x - 2 + √3)

➭Using Identity:- a² - b² = (a + b) (a - b)

➭ Here a = (x - 2) & b = (√3)

➭ (x - 2)² - (√3)²

➭ Using Identity:- (a - b)² = a² - 2ab + b²

➭ x² - 4x + 4 - 3

➭ x² - 4x + 1

Now,

Dividing x⁴ - 6x³ - 26x² + 138x - 35 by x² - 4x + 1

Refer to the attachment:-

Quotient = x² - 2x - 35

Then By Middle Splitting the term..

★ x² - 2x - 35

➙ x² - 7x + 5x - 35

➙ x(x - 7) + 5(x - 7)

➙ (x - 7) (x + 5)

➙ x - 7 = 0 , x + 5 = 0

➙ x = 7 , x = - 5

$\: \fbox{★ \: Hence, 7 and −5 \: are the other zeros of this polynomial}$

Answer 2

Answer:

According to the Question:-

➭ P(x) = x⁴ - 6x³ - 26x² + 138x - 35

➭ x = 2 + √3 , x = 2 - √3

➭ (x - 2 - √3). (x - 2 + √3)

_____________________

Using Identity:-

➭ a² - b² = (a + b) (a - b)

➭ Here a = (x - 2) & b = (√3)

➭ (x - 2)² - (√3)²

Using Identity :-

➭ (a - b)² = a² - 2ab + b²

➭ x² - 4x + 4 - 3

➭ x² - 4x + 1

_____________________

Now,

Dividing

x⁴ - 6x³ - 26x² + 138x - 35 by x² - 4x + 1

Quotient = x² - 2x - 35

_____________________

Then By Middle term split

★ x² - 2x - 35

➙ x² - 7x + 5x - 35

➙ x(x - 7) + 5(x - 7)

➙ (x - 7) (x + 5)

➙ x - 7 = 0 , x + 5 = 0

➙ x = 7 , x = (-5)

_____________________

★ Hence,

7 and (-5) are the other zeros of this polynomial

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Hope it helps you :)

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