To divide the function f(x) by (x^2-4x-12), we find that the quotient is Q(x) and the remainder is (x+6). If f(-2)=a and f(6)=b, what is the value of b/a?
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To find the value of b/a, we first need to determine the values of a and b.
Given that the quotient of dividing f(x) by (x^2-4x-12) is Q(x) and the remainder is (x+6), we can write the following equation:
f(x) = Q(x)(x^2-4x-12) + (x+6)
Since we are given that f(-2) = a, we can substitute x = -2 in the equation:
f(-2) = Q(-2)(-2^2-4(-2)-12) + (-2+6)
a = Q(-2)(4+8-12) + 4
a = Q(-2)(0) + 4
a = 4
Therefore, we've determined that a = 4.
Now, let's find the value of b. Given that f(6) = b, we can substitute x = 6 in the equation:
f(6) = Q(6)(6^2-4(6)-12) + (6+6)
b = Q(6)(36-24-12) + 12
b = Q(6)(0) + 12
b = 12
So, we've determined that b = 12.
Finally, to find the value of b/a, we can substitute the values we found:
b/a = 12/4
b/a = 3
Hence, the value of b/a is 3.