(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

I'm asked to find (a/b) in the simplest form if the co-efficient of x^8 is zero in the expansion of:

(1 + x)(a - bx)^12

2. Relevant equations

Binomial expansion formula ... (a + b)^n = Sum of r --> n (r = 0) (nCr)(a^(n-r) * b^r

3. The attempt at a solution

I figured that x^8 could be achieved from two possible situations ...

either 1 * the expansion of (a - bx)^12 or x * the expansion of (a - bx)^12

I found the value of r at both these points by looking for the value of r that makes bx^r = x^8 and x*bx^r = x^8. This I found to be r = 7 and r = 8. Then I wrote as:

(12C7) * (a)^5 * (-b)^7 + (12C7) * (a)^4 * (-b)^8 = 0

Then I get stuck as I cannot seem to get values for a and b from this.

Can anyone help me?

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# Finding Binomial Co-efficient from pronumerals

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