Find the polynomial having roots at $1$ , $6$ , $- 7$ and $- 2$ .

Answer

The polynomial generated from the given zeros is: $P (x) = x^{4} + 2 x^{3} - 43 x^{2} - 44 x + 84$

Explanation

Step 1: Turn the zeros into factors:

Zero	Factor
$1$	$x - 1$
$6$	$x - 6$
$- 7$	$x + 7$
$- 2$	$x + 2$

Step 2: Multiply the factors together:

P (x) = (x - 1) \cdot (x - 6) \cdot (x + 7) \cdot (x + 2) = x^{4} + 2 x^{3} - 43 x^{2} - 44 x + 84

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Find the polynomial having roots at 1 , 6 , −7 and −2 .

The polynomial generated from the given zeros is: P(x)=x4+2x3−43x2−44x+84

Find the polynomial having roots at $1$ , $6$ , $- 7$ and $- 2$ .

The polynomial generated from the given zeros is: $P (x) = x^{4} + 2 x^{3} - 43 x^{2} - 44 x + 84$