Question

If one root of the quadratic equation x^2-42+1 = 0 is
(2+√3). then the other root is​

Answer 1

Answer:

Other root of your this equation is

$\sqrt{41}$

Answer 2

Answer:

The other factor is (2 - √3)

Step-by-step explanation:

We are given that,

p(x) = x² - 4x + 1

Also,

1 of the roots(alpha) = (2 + √3)

x = (2 + √3)

Then,

(x - (2 + √3)) is a factor,

= x + (-2 - √3)

Thus,

g(x) = x + (-2 - √3)

Now, let's divide p(x) by g(x) to get the other factor

x + (-2 + √3)

___________

x + (-2 - √3) | x² - 4x + 1

– (x² - x(2 - √3))

——————————

0 - 2x + √3x + 1

– (-2x + √3x + 1)

—————————

0

Thus,

The other factor is (x + (-2 + √3))

Hence,

x = -(-2 + √3)

x = 2 - √3

We can also check this using the factors

(x - 2 - √3)(x - 2 + √3)

Using (a + b)(a - b) = a² - b²

= ((x - 2)² - (√3)²

= (x² - 4x + 4) - (3)

= x² - 4x + 4 - 3

= x² - 4x + 1

Thus, it is correct

Hence, the other factor is (2 - √3)

Hope it helped and you understood it........All the best