sorry binomial again, pllssss helllpp (1 Viewer)

yashbb · Sep 27, 2021

sorry for blurry image

Lith_30 · Sep 27, 2021

First we should find the general term of $(1+ax)^{10}$

$\text{General Term}\\\\={10 \choose k}\cdot{a}^{k}\cdot{x}^{k}$

Now since they told us that the coefficient of $x^6$ is 0, we can find $a$ by finding the coefficient of $x^6$ in terms of $a$ .

Since the general term is being multiplied by $(1-2x)$ we multiply the general term by each of the values in the bracket, then find the coefficients of $x^6$ in both cases, then we add them together to find the actual coefficient of $x^6$ .

$\text{First term}\\\\1\cdot{10 \choose k}\cdot{a}^{k}\cdot{x}^{k}$
Since we need to find the coefficient of $x^6$ we let $k=6$ .
${10 \choose 6}\cdot{a}^{6}\cdot{x}^{6}\\\\=210a^6x^6$

$\text{Second term}\\\\-2x\cdot{10 \choose k}\cdot{a}^{k}\cdot{x}^{k}\\\\=-2{10 \choose k}\cdot{a}^{k}\cdot{x}^{k+1}$
Since we need to find the coefficient of $x^6$ we let $k=5$ .
$-2{10 \choose 5}\cdot{a}^{5}\cdot{x}^{5+1}\\\\=-504a^5x^6$

$\therefore \text{Coefficient of } x^6=210a^6-504a^5=0\\\\a^5(210a-504)=0\\a=0,\ a=2.4$

$\therefore a=2.4$

yashbb · Sep 27, 2021

Lith_30 said:
First we should find the general term of $(1+ax)^{10}$

$\text{General Term}\\\\={10 \choose k}\cdot{a}^{k}\cdot{x}^{k}$

Now since they told us that the coefficient of $x^6$ is 0, we can find $a$ by finding the coefficient of $x^6$ in terms of $a$ .

Since the general term is being multiplied by $(1-2x)$ we multiply the general term by each of the values in the bracket, then find the coefficients of $x^6$ in both cases, then we add them together to find the actual coefficient of $x^6$ .

$\text{First term}\\\\1\cdot{10 \choose k}\cdot{a}^{k}\cdot{x}^{k}$
Since we need to find the coefficient of $x^6$ we let $k=6$ .
${10 \choose 6}\cdot{a}^{6}\cdot{x}^{6}\\\\=210a^6x^6$

$\text{Second term}\\\\-2x\cdot{10 \choose k}\cdot{a}^{k}\cdot{x}^{k}\\\\=-2{10 \choose k}\cdot{a}^{k}\cdot{x}^{k+1}$
Since we need to find the coefficient of $x^6$ we let $k=5$ .
$-2{10 \choose 5}\cdot{a}^{5}\cdot{x}^{5+1}\\\\=-504a^5x^6$

$\therefore \text{Coefficient of } x^6=210a^6-504a^5=0\\\\a^5(210a-504)=0\\a=0,\ a=2.4$

$\therefore a=2.4$

thank you so much!!!!

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sorry binomial again, pllssss helllpp (1 Viewer)

yashbb

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Lith_30

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yashbb

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