Question

Write two polynomials that have 3 zeroes each?

Answer 1

$1. \: \: \: {x}^{3} - x \\ 2. \: \: {x}^{3} \ + 3 {x}^{2} + 2$

Answer 2

Answer:

$x^3-3x^2+2x$

$x^3+3x^2+2x$

Step-by-step explanation:

The number of zeros of a polynomial should be equal to the degree of the polynomial.

Since, the number of zeros is three hence, the degree of the polynomial must be 3. And it is a cubic polynomial.

First polynomial:

Let zeros of the polynomial is 0, 1, 2

Then the polynomial is given by

$(x-0)(x-1)(x-2)\\\\=x^3-3x^2+2x$

Second polynomial:

Let zeros of the polynomial is 0, -1, -2

Then the polynomial is given by

$(x-0)(x+1)(x+2)\\\\=x^3+3x^2+2x$