Find the polynomial having roots at $3$ , $4$ , $5$ and $6$ .

Answer

The polynomial generated from the given zeros is: $P (x) = x^{4} - 18 x^{3} + 119 x^{2} - 342 x + 360$

Explanation

Step 1: Turn the zeros into factors:

Zero	Factor
$3$	$x - 3$
$4$	$x - 4$
$5$	$x - 5$
$6$	$x - 6$

Step 2: Multiply the factors together:

P (x) = (x - 3) \cdot (x - 4) \cdot (x - 5) \cdot (x - 6) = x^{4} - 18 x^{3} + 119 x^{2} - 342 x + 360

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Find the polynomial having roots at 3 , 4 , 5 and 6 .

The polynomial generated from the given zeros is: P(x)=x4−18x3+119x2−342x+360

Find the polynomial having roots at $3$ , $4$ , $5$ and $6$ .

The polynomial generated from the given zeros is: $P (x) = x^{4} - 18 x^{3} + 119 x^{2} - 342 x + 360$