Question

write polynomial zeros: -2,-1,2,4 degree:4

Answer 1

Answer:

The required polynomial is $x^4-3x^3-8x^2+12x+16$

Step-by-step explanation:

To find the polynomial when the zeros or the roots are given for example, $a_1, a_2, ....a_n$, then the polynomial will be given by $\left(x-a_1\right)\left(x-a_2\right).......\left(x-a_n\right)$.

So here also we will use this concept. Now the zeros of the polynomials is:

-2,-1,2,4, so these are the values of x here, and the polynomial is written as

$\left(x+2\right)\left(x+1\right)\left(x-2\right)\left(x-4\right)$

Now, we will open the brackets to get the final polynomial expression, as follows:

$\left(x+2\right)\left(x+1\right)\left(x-2\right)\left(x-4\right)\\=\left(x^2+3x+2\right)\left(x-2\right)\left(x-4\right)\\=\left(x^3+x^2-4x-4\right)\left(x-4\right)\\=x^4-3x^3-8x^2+12x+16$

So the required polynomial is formed.