Find the polynomial having roots at $8$ , $9$ , $5$ , $4$ , $- 3$ , $- 54$ and $1$ .

Answer

The polynomial generated from the given zeros is: $P (x) = x^{7} + 30 x^{6} - 1106 x^{5} + 9840 x^{4} - 23951 x^{3} - 62790 x^{2} + 311256 x - 233280$

Explanation

Step 1: Turn the zeros into factors:

Zero	Factor
$8$	$x - 8$
$9$	$x - 9$
$5$	$x - 5$
$4$	$x - 4$
$- 3$	$x + 3$
$- 54$	$x + 54$
$1$	$x - 1$

Step 2: Multiply the factors together:

P (x) = (x - 8) \cdot (x - 9) \cdot (x - 5) \cdot (x - 4) \cdot (x + 3) \cdot (x + 54) \cdot (x - 1) = x^{7} + 30 x^{6} - 1106 x^{5} + 9840 x^{4} - 23951 x^{3} - 62790 x^{2} + 311256 x - 233280

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Find the polynomial having roots at 8 , 9 , 5 , 4 , −3 , −54 and 1 .

The polynomial generated from the given zeros is: P(x)=x7+30x6−1106x5+9840x4−23951x3−62790x2+311256x−233280

Find the polynomial having roots at $8$ , $9$ , $5$ , $4$ , $- 3$ , $- 54$ and $1$ .

The polynomial generated from the given zeros is: $P (x) = x^{7} + 30 x^{6} - 1106 x^{5} + 9840 x^{4} - 23951 x^{3} - 62790 x^{2} + 311256 x - 233280$