Find the polynomial having roots at $10$ , $20$ , $30$ , $40$ , $50$ and $60$ .

Answer

The polynomial generated from the given zeros is: $P (x) = x^{6} - 210 x^{5} + 17500 x^{4} - 735000 x^{3} + 16240000 x^{2} - 176400000 x + 720000000$

Explanation

Step 1: Turn the zeros into factors:

Zero	Factor
$10$	$x - 10$
$20$	$x - 20$
$30$	$x - 30$
$40$	$x - 40$
$50$	$x - 50$
$60$	$x - 60$

Step 2: Multiply the factors together:

P (x) = (x - 10) \cdot (x - 20) \cdot (x - 30) \cdot (x - 40) \cdot (x - 50) \cdot (x - 60) = x^{6} - 210 x^{5} + 17500 x^{4} - 735000 x^{3} + 16240000 x^{2} - 176400000 x + 720000000

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Find the polynomial having roots at 10 , 20 , 30 , 40 , 50 and 60 .

The polynomial generated from the given zeros is: P(x)=x6−210x5+17500x4−735000x3+16240000x2−176400000x+720000000

Find the polynomial having roots at $10$ , $20$ , $30$ , $40$ , $50$ and $60$ .

The polynomial generated from the given zeros is: $P (x) = x^{6} - 210 x^{5} + 17500 x^{4} - 735000 x^{3} + 16240000 x^{2} - 176400000 x + 720000000$