Find the polynomial having roots at $2$ , $3$ , $4$ and $- 7$ .

Answer

The polynomial generated from the given zeros is: $P (x) = x^{4} - 2 x^{3} - 37 x^{2} + 158 x - 168$

Explanation

Step 1: Turn the zeros into factors:

Zero	Factor
$2$	$x - 2$
$3$	$x - 3$
$4$	$x - 4$
$- 7$	$x + 7$

Step 2: Multiply the factors together:

P (x) = (x - 2) \cdot (x - 3) \cdot (x - 4) \cdot (x + 7) = x^{4} - 2 x^{3} - 37 x^{2} + 158 x - 168

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Find the polynomial having roots at 2 , 3 , 4 and −7 .

The polynomial generated from the given zeros is: P(x)=x4−2x3−37x2+158x−168

Find the polynomial having roots at $2$ , $3$ , $4$ and $- 7$ .

The polynomial generated from the given zeros is: $P (x) = x^{4} - 2 x^{3} - 37 x^{2} + 158 x - 168$