How do you find a polynomial of degree 3 that has zeros of -3, 0, 1?

Question

How do you find a polynomial of degree 3 that has zeros of -3, 0, 1?

1 Answer

Impact of this question

61475 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-11-15T00:59:37

$P (x) = x^{3} + 2 x^{2} - 3 x$ $P(x)=x^3+2x^2-3x$

Explanation:

A polynomial has $α$ $alpha$ as a zero if and only if $(x - α)$ $(x-alpha)$ is a factor of the polynomial. Working backwards, then, we can generate a polynomial with any zeros we desire by multiplying such factors.

We want a polynomial $P (x)$ $P(x)$ with zeros $- 3, 0, 1$ $-3, 0, 1$ , so:

$P (x) = (x - (- 3)) (x - 0) (x - 1)$ $P(x) = (x-(-3))(x-0)(x-1)$

$= (x + 3) x (x - 1)$ $=(x+3)x(x-1)$

$= x (x + 3) (x - 1)$ $=x(x+3)(x-1)$

$= x (x^{2} + 2 x - 3)$ $=x(x^2+2x-3)$

$= x^{3} + 2 x^{2} - 3 x$ $=x^3+2x^2-3x$

Note that we could also multiply by any nonzero constant without changing the zeros, if a different polynomial is desired.

Science

Math

Humanities

... and beyond

How do you find a polynomial of degree 3 that has zeros of -3, 0, 1?

1 Answer

Explanation:

Related questions

Impact of this question