Question

please answer this question i need the process please​

Answer 1

Solution :

The given equation is

x³ - 5x² + 9x - 5 = 0 .....(i)

Since (2 + i) is a root of (i), it is a certain that (2 - i) will be another root.

Then, {x - (2 + i)} {x - (2 - i)} is a factor of (i)

= x² - (2 - i + 2 + i) x + (2+ i)(2 - i)

= x² - 4x + (4 - i²)

= x² - 4x + 5

Now, x³ - 5x² + 9x - 5 = 0

    ⇒ x³ - 4x² + 5x - x² + 4x - 5 = 0

    ⇒ x (x² - 4x + 5) - (x² - 4x + 5) = 0

    ⇒ (x² - 4x + 5) (x - 1) = 0

Either x² - 4x + 5 = 0 or, x - 1 = 0

So, another root = 1

Hence, the other two roots are (2 - i) and 1

∴ Option (1) is correct.