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

Answer

The polynomial generated from the given zeros is: $P (x) = x^{3} - 6 x^{2} - 19 x + 84$

Explanation

Step 1: Turn the zeros into factors:

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

Step 2: Multiply the factors together:

P (x) = (x - 3) \cdot (x - 7) \cdot (x + 4) = x^{3} - 6 x^{2} - 19 x + 84

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

The polynomial generated from the given zeros is: P(x)=x3−6x2−19x+84

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

The polynomial generated from the given zeros is: $P (x) = x^{3} - 6 x^{2} - 19 x + 84$