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

Answer

The polynomial generated from the given zeros is: $P (x) = x^{3} + 8 x^{2} + x - 42$

Explanation

Step 1: Turn the zeros into factors:

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

Step 2: Multiply the factors together:

P (x) = (x - 2) \cdot (x + 7) \cdot (x + 3) = x^{3} + 8 x^{2} + x - 42

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

The polynomial generated from the given zeros is: P(x)=x3+8x2+x−42

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

The polynomial generated from the given zeros is: $P (x) = x^{3} + 8 x^{2} + x - 42$