Question

if one zero of the polynomial x square - 4 x + 1 is 2 + root 3 write the other Hero

Answer 1

Answer:

$\large{\pink{2 - \sqrt{3}}}$

Step-by-step explanation:

Question:

If onw zero of the polynomial x^2 - 4x + 1 is $2 + \sqrt{3}$. Write the other zero.

Given polynomial:

x^2 - 4x + 1

Given zero: $2 + \sqrt{3}$

To find: the other zero

As it a quadratic polynomial, therefore it must have two zeroes.

x^2 - 4x + 1 = 0

Comparing the the equation with ax^2 + bx + c = 0, we obtain,

a = 1; b = - 4; c = 1

By using quadratic formula,

$\large{\bold{x = \frac{- b \pm \sqrt{b^2 - 4ac}}{2a}}}$

$x = \large{\frac{-(-4) \pm \sqrt{(-4)^2 - 4 \times 1 \times 1}}{2(1)}}$

$x = \large{\frac{4 \pm \sqrt{16 - 4}}{2}}$

$x = \large{\frac{4 \pm \sqrt{12}}{2}}$

$x = \large{\frac{4 \pm 2 \sqrt{3}}{2}}$

$x = \large{\frac{2 (2 \pm \sqrt{3})} {2}}$

$x = \large{\frac{\cancel{2}(2 \pm \sqrt{3})}{\cancel{2}}}$

$x = 2 \pm \sqrt{3}$

$\therefore \boxed{\green{x = 2 + \sqrt{3} \:or\: 2 - \sqrt{3}}}$

Since, given one zero is $2 + \sqrt{3}$,

Therefore, the next zero must be $\bold{2 - \sqrt{3}}$.