Question

Write a polynomial equation of degree 3 such that two of its roots are 2 and an imaginary number.

Answer 1

hope you get it

X^3-2x^2+ x-2

Answer 2

The required polynomial is
`x^3-2x^2+x-2`

Step-by-step explanation:

Given : A polynomial equation of degree 3 such that two of its roots are 2 and an imaginary number.

To find : The equation of polynomial with degree 3.

Solution :

It is given that the equation has 3 roots one is 2 and othe is imaginary.

So, one root 2 = (x-2)

Let the other two roots are imaginary i, -i

⇒ (x-i),(x+i)

Therefore, the roots of the polynomial of degree 3

`(x-2)(x-i)(x+i)`

Now, we solve the roots to find the equation,

`\Rightarrow(x-2)(x^2+xi-xi-i^2)`

`\Rightarrow(x-2)(x^2+i^2)`
`[i^2=-1]`

`\Rightarrow(x^3+x-2x^2-2)`

`\Rightarrow x^3-2x^2+x-2`

Therefore, the required polynomial is
`x^3-2x^2+x-2`