Question

Write a polynomial given the zeros of 0 (multiplicity 2), 1

Answer 1

`\displaystyle{P(x)=x^3-x^2}`

Explanation:

Given the zeros of 0, 0, 1. We can write the polynomial in form of x-intersects:

`\displaystyle{P(x) = (x-x_1)(x-x_2)(x-x_3)}`

Hence:

`\displaystyle{P(x)=(x-0)(x-0)(x-1)}`

Which can be simplified to:

`\displaystyle{P(x)=x\cdot x \cdot (x-1)}\\\\\displaystyle{P(x)=x^2(x-1)}`

Convert to the standard form by distributing x²:

`\displaystyle{P(x)=x^2\cdot x - x^2 \cdot 1}\\\\\displaystyle{P(x)=x^3-x^2}`