Question

Write the polynomial in standard form that has zeros at X=4/5 and 0 (mult. 2).

a) 5x^2 - 4
b) 5x^2 - 4x
c) 5x^2 + 4
d) 5x^2 - 4x^2

Answer 1

To find the polynomial in standard form with given zeros, multiply the factors of the zeros together. The polynomial in standard form is X³ - (4/5)X².

Step-by-step explanation:

To find the polynomial in standard form with given zeros, we first write the zeros as factors of the polynomial. The zeros are X = 4/5 and X = 0 (with a multiplicity of 2).

So the factors of the polynomial are (X - 4/5) and (X - 0)(X - 0) which simplify to (X - 4/5) and X².

To get the polynomial in standard form, we multiply the factors together. (X - 4/5)(X²) = X³ - (4/5)X² which is the polynomial in standard form with the given zeros.