Find the polynomial having roots at $- 1$ , $2$ , $7$ and $- 3$ .

Answer

The polynomial generated from the given zeros is: $P (x) = x^{4} - 5 x^{3} - 19 x^{2} + 29 x + 42$

Explanation

Step 1: Turn the zeros into factors:

Zero	Factor
$- 1$	$x + 1$
$2$	$x - 2$
$7$	$x - 7$
$- 3$	$x + 3$

Step 2: Multiply the factors together:

P (x) = (x + 1) \cdot (x - 2) \cdot (x - 7) \cdot (x + 3) = x^{4} - 5 x^{3} - 19 x^{2} + 29 x + 42

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Find the polynomial having roots at −1 , 2 , 7 and −3 .

The polynomial generated from the given zeros is: P(x)=x4−5x3−19x2+29x+42

Find the polynomial having roots at $- 1$ , $2$ , $7$ and $- 3$ .

The polynomial generated from the given zeros is: $P (x) = x^{4} - 5 x^{3} - 19 x^{2} + 29 x + 42$