Question

If one zeros of the polynomial x2 -4x+1 is 2+ √3,write the other zeros

Answer 1

Given that,

If one zeros of the polynomial x² - 4x + 1 is 2+ √3,write the other zero.

Let

• a = 1
• b = -4
• c = 1
• α = 2 + √3

Sum of the zeroes : α + ß = -b/a

Substitute the zeroes..

$⟹ \alpha + \beta = \frac{ - b}{a} \\ \\ ⟹ \alpha + 2 + \sqrt{3} = \frac{ - ( - 4)}{1} \\ \\ ⟹ \alpha + 2 + \sqrt{3} = 4 \\ \\ ⟹ \alpha + \sqrt{3} = 4 - 2 \\ \\ ⟹ \alpha + \sqrt{3} = 2 \\ \\ ⟹ \alpha = 2 - \sqrt{3}$

Therefore,the another zero is “ 2 - √3 ” .

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