Find the polynomial having roots at $1$ , $- 5$ and $- 2$ .

Answer

The polynomial generated from the given zeros is: $P (x) = x^{3} + 6 x^{2} + 3 x - 10$

Explanation

Step 1: Turn the zeros into factors:

Zero	Factor
$1$	$x - 1$
$- 5$	$x + 5$
$- 2$	$x + 2$

Step 2: Multiply the factors together:

P (x) = (x - 1) \cdot (x + 5) \cdot (x + 2) = x^{3} + 6 x^{2} + 3 x - 10

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Find the polynomial having roots at 1 , −5 and −2 .

The polynomial generated from the given zeros is: P(x)=x3+6x2+3x−10

Find the polynomial having roots at $1$ , $- 5$ and $- 2$ .

The polynomial generated from the given zeros is: $P (x) = x^{3} + 6 x^{2} + 3 x - 10$