Question

Find a polynomial of the smallest degree with integer coefficient whose zeros are 0, 2 and 7

Answer 1

Explanation:

`P(x)=x*(x-2)*(x-7)=x^3-9x^2+14x\\`

The polynomial of the smallest degree with integer coefficients whose zeros are 0, 2, and 7 can be found by using the zero product property.

Since the zeros are 0, 2, and 7, we can write the polynomial as:

(x - 0)(x - 2)(x - 7)

Simplifying this expression, we get:

x(x - 2)(x - 7)

Expanding this expression, we have:

`x(x^2 - 2x - 7x + 14)`

Combining like terms, we get:

`x(x^2 - 9x + 14)`

Multiplying further, we have:

`x^3 - 9x^2 + 14x`

Therefore, the polynomial of the smallest degree with integer coefficients whose zeros are 0, 2, and 7 is:

`x^3 - 9x^2 + 14x\\`