Find the polynomial having roots at $- 1$ , $7$ and $8$ .

Answer

The polynomial generated from the given zeros is: $P (x) = x^{3} - 14 x^{2} + 41 x + 56$

Explanation

Step 1: Turn the zeros into factors:

Zero	Factor
$- 1$	$x + 1$
$7$	$x - 7$
$8$	$x - 8$

Step 2: Multiply the factors together:

P (x) = (x + 1) \cdot (x - 7) \cdot (x - 8) = x^{3} - 14 x^{2} + 41 x + 56

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Find the polynomial having roots at −1 , 7 and 8 .

The polynomial generated from the given zeros is: P(x)=x3−14x2+41x+56

Find the polynomial having roots at $- 1$ , $7$ and $8$ .

The polynomial generated from the given zeros is: $P (x) = x^{3} - 14 x^{2} + 41 x + 56$