#ALGEBRA help please
twin whale
opal pewter
This is an equation of degree 21. So, it has 21 roots.
10 roots are 2i. As the coefficients are real, 10 more roots must be -2i. Thus, we have 1 root left. Let's call it a.
Then the equation becomes:
(x - a)(x^2 + 4)^10 = 0
We need the coefficient near x^9. We can only obtain it after expanding the second factor and multiplying the x^8 term from it by x from the first term.
Thus, we need to find the coefficient of the x^8 term from the second factor.
As x^8 = (x^2)^4, that term is 4^(10 - 4)C(10, 4) = 4^6 C(10, 4).
twin whale
THANK YOU SO MUCH that's really helpful ❤️
opal pewter
You're welcome!
twin whale
May I ask what if the required coeff was for X^(an even #), then I need to get the value of (a) right? How can I get that?
@opal pewter
opal pewter
May I ask what if the required coeff was for X^(an even #), then I need to get t...
No, as when we multiply a by terms of the second factor, they will all have even powers.
And we are looking for the coefficient of the term with an odd power.
So, all even terms will have coefficients dependent on a, while all the odd terms will have coefficients independent of a.
twin whale
Oh yes
But is there a way I can deduce the value of a in case I need to determine the value of a coeffinient for an even power of case?
Given that a21=1 , may this be any helpful to get a?