How do you find a polynomial function of degree $4$ with $- 4$ as a zero of multiplicity $3$ and $0$ as a zero of multiplicity $1$ ?

Open in App

Solution

Polynomial function:
Given zeros are $x = - 4$ (multiply $3$ ) and at $x = 0$ (multiply $1$ )
Since the zeros $x = - 4$ have a multiplicity of three, we can write it as the factor $(x + 4)$ raised to the third power.
$f (x) = {(x + 4)}^{3}$
And there is also zero at $x = 0$ , so we can add an $x$ .
$f (x) = x {(x + 4)}^{3}$
In expanded form, is
$f (x) = x^{4} + 12 x^{3} + 48 x^{2} + 64 x$
Hence, the polynomial function of degree $4$ with $- 4$ as a zero of multiplicity $3$ and $0$ as a zero of multiplicity $1$ is
$f (x) = x^{4} + 12 x^{3} + 48 x^{2} + 64 x$

Suggest Corrections

Similar questions

How do you write a polynomial with Zeros: $- 2$ , multiplicity $2$ ; $4$ , multiplicity $1$ ; degree $3$ ?

How do you find the polynomial function with a leading coefficient $2$ that has the given degree and zeroes: degree $3$ , zeroes $- 2, 1, 4$ ?

Find the polynomial function $f (x)$ of least degree having only real coefficients and zeros as given.

Assume multiplicity $1$ .

$0, - i and 2 + i$ .

How do you find a polynomial function that has zeros $x = - 5, 1, 2$ and degree $n = 4$ .

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

Join BYJU'S Learning Program