How do you find a polynomial function that has zeros $x = - 4, - 1, 3, 6$ $x=-4, -1, 3, 6$ and degree n=4?

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Answer 1 · 2017-01-25T18:53:39

The Reqd. Poly. Fun. is

$k(x^4-4x^3-23x^2+54x+2), k in RR-{0}.$

Let us denote by $p(x)$ the reqd. poly. fun.

$x=-4" is a zero of "p(x):. (x-(-4))=(x+4)$ is a factor.

On the similar lines, $(x+1), (x-3) and (x-6)$ are also factors.

As the degree of $p(x)$ is $4,$ $p(x)$ can not have any more

factors, except some constant, say, $k!=0$ .

Accordingly, we have,

$p(x)=k(x+4)(x+1)(x-3)(x-6)$

$=k{(x+4)(x-6)}(x+1)(x-3)$

$=k{(x^2-2x-24)(x^2-2x-3)}$

$=k(y-24)(y-3), [y=x^2-2x]$

$=k(y^2-27y+72)$

$=k{(x^2-2x)^2-27(x^2-2x)+72}$

$=k{x^4-4x^3+4x^2-27x^2+54x+72}$

$:. p(x)=k(x^4-4x^3-23x^2+54x+2), k in RR-{0},$ is the reqd. poly.

Enjoy Maths.!

How do you find a polynomial function that has zeros x=-4, -1, 3, 6x=−4,−1,3,6x=-4, -1, 3, 6 and degree n=4?