Question

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

Answer 1

Answer:

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 $x^3-2x^2+x-2$  

Answer 2

 hope you get it 

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