How do you find the polynomial function with leading coefficient 2 that has the given degree and zeroes: degree 3: zeroes 2, 1/2, 3/2?

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How do you find the polynomial function with leading coefficient 2 that has the given degree and zeroes: degree 3: zeroes 2, 1/2, 3/2?

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Answer 1 · 2016-09-04T09:29:41

The polynomial function is
$2 x^{3} - 8 x^{2} + \frac{19}{2} x - 3$ $2x^3-8x^2+19/2x-3$

Explanation:

A polynomial function with zeros as $a$ $a$ , $b$ $b$ and $c$ $c$ can be written as

$(x - a) (x - b) (x - c)$ $(x-a)(x-b)(x-c)$

However, this will give the leading coefficient as $1$ $1$ . If leading coefficient is $n$ $n$ , the polynomial would be $n (x - a) (x - b) (x - c)$ $n(x-a)(x-b)(x-c)$ .

Hence a polynomial function of degree $3$ $3$ , zeros $2$ $2$ , $\frac{1}{2}$ $1/2$ and $\frac{3}{2}$ $3/2$ and leading coefficient $2$ $2$ is

$2 (x - 2) (x - \frac{1}{2}) (x - \frac{3}{2})$ $2(x-2)(x-1/2)(x-3/2)$

= $2 (x - 2) (x^{2} - 2 x + \frac{3}{4})$ $2(x-2)(x^2-2x+3/4)$

= $2 (x^{3} - 2 x^{2} + \frac{3}{4} x - 2 x^{2} + 4 x - \frac{3}{2})$ $2(x^3-2x^2+3/4x-2x^2+4x-3/2)$

= $2 x^{3} - 8 x^{2} + \frac{19}{2} x - 3$ $2x^3-8x^2+19/2x-3$

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How do you find the polynomial function with leading coefficient 2 that has the given degree and zeroes: degree 3: zeroes 2, 1/2, 3/2?

1 Answer

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