Find the polynomial having roots at $1$ , $2$ , $3$ and $- 4$ .

Answer

The polynomial generated from the given zeros is: $P (x) = x^{4} - 2 x^{3} - 13 x^{2} + 38 x - 24$

Explanation

Step 1: Turn the zeros into factors:

Zero	Factor
$1$	$x - 1$
$2$	$x - 2$
$3$	$x - 3$
$- 4$	$x + 4$

Step 2: Multiply the factors together:

P (x) = (x - 1) \cdot (x - 2) \cdot (x - 3) \cdot (x + 4) = x^{4} - 2 x^{3} - 13 x^{2} + 38 x - 24

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Find the polynomial having roots at 1 , 2 , 3 and −4 .

The polynomial generated from the given zeros is: P(x)=x4−2x3−13x2+38x−24

Find the polynomial having roots at $1$ , $2$ , $3$ and $- 4$ .

The polynomial generated from the given zeros is: $P (x) = x^{4} - 2 x^{3} - 13 x^{2} + 38 x - 24$