Find the polynomial having roots at $- 3$ , $- 3$ , $1$ , $4$ and $5$ .

Answer

The polynomial generated from the given zeros is: $P (x) = x^{5} - 4 x^{4} - 22 x^{3} + 64 x^{2} + 141 x - 180$

Explanation

Step 1: Turn the zeros into factors:

Zero	Factor
$- 3$	$x + 3$
$- 3$	$x + 3$
$1$	$x - 1$
$4$	$x - 4$
$5$	$x - 5$

Step 2: Multiply the factors together:

P (x) = (x + 3) \cdot (x + 3) \cdot (x - 1) \cdot (x - 4) \cdot (x - 5) = x^{5} - 4 x^{4} - 22 x^{3} + 64 x^{2} + 141 x - 180

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Find the polynomial having roots at −3 , −3 , 1 , 4 and 5 .

The polynomial generated from the given zeros is: P(x)=x5−4x4−22x3+64x2+141x−180

Find the polynomial having roots at $- 3$ , $- 3$ , $1$ , $4$ and $5$ .

The polynomial generated from the given zeros is: $P (x) = x^{5} - 4 x^{4} - 22 x^{3} + 64 x^{2} + 141 x - 180$