Question

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

1 point

2 + √3

2 - √3

-2 + √3

-2 - √3

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Answer 1

Answer:

Given that,

p(x) = x² - 4x + 1

One of zero = 2 + √3

To find,

Other zero = ?

Assumption:

Let α = 2 + √3 and β be the other zero.

As we know, it's a quadratic equation, so it should have maximum two zeros.

By using the relationship between the co-efficients and the zeros of a quadratic equation,

(i) α + β = - b/a

(2 + √3) + β = -(-4)/1

(2 + √3) + β = 4/1

√3 + β = 4/1 - 2

√3 + β = 2/1

β = 2 - √3

So, the other zero is 2 - √3 .

Step-by-step explanation:

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