Find the polynomial having roots at $3$ , $4$ , $7$ , $- 2$ and $0$ .

Answer

The polynomial generated from the given zeros is: $P (x) = x^{5} - 12 x^{4} + 33 x^{3} + 38 x^{2} - 168 x$

Explanation

Step 1: Turn the zeros into factors:

Zero	Factor
$3$	$x - 3$
$4$	$x - 4$
$7$	$x - 7$
$- 2$	$x + 2$
$0$	$x$

Step 2: Multiply the factors together:

P (x) = (x - 3) \cdot (x - 4) \cdot (x - 7) \cdot (x + 2) \cdot x = x^{5} - 12 x^{4} + 33 x^{3} + 38 x^{2} - 168 x

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Find the polynomial having roots at 3 , 4 , 7 , −2 and 0 .

The polynomial generated from the given zeros is: P(x)=x5−12x4+33x3+38x2−168x

Find the polynomial having roots at $3$ , $4$ , $7$ , $- 2$ and $0$ .

The polynomial generated from the given zeros is: $P (x) = x^{5} - 12 x^{4} + 33 x^{3} + 38 x^{2} - 168 x$