Here we are given that a polynomial has zeros as 2 , i and -i . We need to find out the cubic polynomial . In general we know that if $\alpha , \ \beta \ \& \ \gamma$ are the zeros of the cubic polynomial , then ,

$\sf \longrightarrow p(x)= (x -\alpha )(x-\beta)(x-\gamma)$

Here in place of the Greek letters , substitute 2,i and -i , we get ,

$\sf\longrightarrow p(x)= (x -2 )(x-i)(x+i)$

Now multiply (x-i) and (x+i ) using the identity (a+b)(a-b)=a² - b² , we have ,

$\sf \longrightarrow p(x)= (x-2)\{ x^2 - (i)^2\}$

Simplify using i = √-1 ,

$\sf \longrightarrow p(x)= (x-2)( x^2 + 1 )$

Multiply by distribution ,

$\sf \longrightarrow p(x)= x(x^2+1) -2(x^2+1)$

Simplify by opening the brackets ,

$\sf\longrightarrow p(x)= x^3+x-2x^2-2$

Rearrange ,

$\sf\longrightarrow \underline{\boxed{\blue{\sf p(x)= x^3-2x^2+x-2}}}$

4 0

2 years ago

Which one<br> also whats 473+838=

Mashutka [201]

Answer:

1,311

Step-by-step explanation:

7 0

3 years ago

Read 2 more answers

If you could help I would really appreciate it, but if not that’s fine. Thank you.

dolphi86 [110]

Answer:

Step-by-step explanation:

j(2) means that x equals 2...

the first inequality in the function says that x is greater than or equal to 2

the second inequality states that x is greater than 2(not equal to) and is less than or equal to 5

the third one states that x is greater than 5

x applies to the first inequality since we know that x can be equal to 2

Now, to the number before the if

there is a 3 before the if in the first inequality

This means that if x is greater than or equal to 2 the y or the function would equal 3

therefore, j(2) would equal 3

I hope this helps!!!

6 0

3 years ago