Find the polynomial having roots at $1$ , $- 7$ and $- 5$ .

Answer

The polynomial generated from the given zeros is: $P (x) = x^{3} + 11 x^{2} + 23 x - 35$

Explanation

Step 1: Turn the zeros into factors:

Zero	Factor
$1$	$x - 1$
$- 7$	$x + 7$
$- 5$	$x + 5$

Step 2: Multiply the factors together:

P (x) = (x - 1) \cdot (x + 7) \cdot (x + 5) = x^{3} + 11 x^{2} + 23 x - 35

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Find the polynomial having roots at 1 , −7 and −5 .

The polynomial generated from the given zeros is: P(x)=x3+11x2+23x−35

Find the polynomial having roots at $1$ , $- 7$ and $- 5$ .

The polynomial generated from the given zeros is: $P (x) = x^{3} + 11 x^{2} + 23 x - 35$