Find the polynomial having roots at $0$ , $5$ , $- 8$ and $7$ .

Answer

The polynomial generated from the given zeros is: $P (x) = x^{4} - 4 x^{3} - 61 x^{2} + 280 x$

Explanation

Step 1: Turn the zeros into factors:

Zero	Factor
$0$	$x$
$5$	$x - 5$
$- 8$	$x + 8$
$7$	$x - 7$

Step 2: Multiply the factors together:

P (x) = x \cdot (x - 5) \cdot (x + 8) \cdot (x - 7) = x^{4} - 4 x^{3} - 61 x^{2} + 280 x

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Find the polynomial having roots at 0 , 5 , −8 and 7 .

The polynomial generated from the given zeros is: P(x)=x4−4x3−61x2+280x

Find the polynomial having roots at $0$ , $5$ , $- 8$ and $7$ .

The polynomial generated from the given zeros is: $P (x) = x^{4} - 4 x^{3} - 61 x^{2} + 280 x$