Question

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

Answer 1

Question:

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

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.

Answer 2

The other zero is $2-\sqrt{3}$.

Step-by-step explanation:

Given : If one zero of the polynomial $x^2-4x+1$ is $2+\sqrt{3}$.

To find : Write the other zero ?

Solution :

Let the polynomial be P(x)=x^2-4x+1

The relation between zeros of polynomial is $\alpha+\beta=-\frac{b}{a}$

One of zero is $\alpha =2+\sqrt{3}$

Here, a=1, b=-4 and c=1

Substitute in the relation,

$2+\sqrt3+\beta=-\frac{-4}{1}$

$2+\sqrt3+\beta=4$

$\beta=4-2-\sqrt3$

$\beta=2-\sqrt3$

Therefore, the other zero is $2-\sqrt{3}$.

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