Find the polynomial having roots at $0$ , $30$ , $45$ and $100$ .

Answer

The polynomial generated from the given zeros is: $P (x) = x^{4} - 175 x^{3} + 8850 x^{2} - 135000 x$

Explanation

Step 1: Turn the zeros into factors:

Zero	Factor
$0$	$x$
$30$	$x - 30$
$45$	$x - 45$
$100$	$x - 100$

Step 2: Multiply the factors together:

P (x) = x \cdot (x - 30) \cdot (x - 45) \cdot (x - 100) = x^{4} - 175 x^{3} + 8850 x^{2} - 135000 x

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Find the polynomial having roots at 0 , 30 , 45 and 100 .

The polynomial generated from the given zeros is: P(x)=x4−175x3+8850x2−135000x

Find the polynomial having roots at $0$ , $30$ , $45$ and $100$ .

The polynomial generated from the given zeros is: $P (x) = x^{4} - 175 x^{3} + 8850 x^{2} - 135000 x$