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Given the pol...

Question

Given the polynomial $a_{0} x^{n} + a_{1} x^{n - 1} + . . . + a_{n - 1} x + a_{n}$ , where $n$ is a positive integer or zero, and $a_{0}$ is a positive integer. The remaining $a^{'} s$ are integers or zero. Set $h = n + a_{0} + | a_{1} | + | a_{2} | + . . . . + | a_{n} |$ . The number of polynomials with $h = 3$ is

3

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5

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6

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7

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9

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Solution

The correct option is A $5$
For $h = 3$ we can have $1 x^{2}, 1 x^{1} + 1, 1 x^{1} - 1, 2 x^{1}, 3 x^{0}$ .

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Similar questions

f (x) = a_{0} x^{n} + a_{1} x^{n - 1} + . . . + a_{n - 1} x + a_{n}, where a_{0}, a_{1}, a_{2}, . . ., a_{n}

a_{0} = a_{1} = a_{2} = . . . = a_{n - 1} = 0 and a_{n} \neq 0,

n

{(1 + x)}^{n} = a_{0} + a_{1} x + a_{2} x^{2} + \dots + a_{n} x^{n}

a_{0} + a_{1} + a_{2} + \dots + a_{n}

\frac{a_{0}}{n + 1} + \frac{a_{1}}{n} + \frac{a_{2}}{n - 1} + . . . . . . + \frac{a_{n - 1}}{2} + a_{n} = 0

a_{0} x^{n} + a_{1} x^{n - 1} + . . . . . . . + . . . . . . + a_{n - 1} x + a_{n} = 0

n > 2

p (x) = x^{n} + a_{n - 1} x^{n - 1} + . . . . . + a_{1} x + a_{0}

a_{0}, a_{1}, . . . . . a_{n - 1}

n p (x) = (1 + x) p^{'} (x)

b = p (1)

{(1 + x + x^{2})}^{n} = 2 n \sum r = 0 a_{r} x^{r}

a_{0} + a_{1} + a_{2} + a_{3} \dots a_{n - 1}

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