To divide the function f(x) by (x2-4x-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?
I recall oobleck answering this yesterday, but with the "search" feature of this webpage being useless I can't find it, I will do it
f(x) / (x^2 - 4x - 12) = Q(x) + (x+6)/(x^2 - 4x - 12)
did you notice x^2 - 4x - 12 = (x-6)(x+2) ??
multiply each term by that denominator
f(x) = Q(x) * ((x-6)(x+2)) + x+6
f(-2) = 0 + -2+6 = a,
so a = 4
f(6) - 0 + 6+6 = b,
so b = 12
then b/a = 12/4 = 3
help plz
To find the value of b/a, we need to determine the values of a and b first. We are given that the remainder obtained when dividing f(x) by (x^2 - 4x - 12) is (x + 6). From this information, we can extract two equations using the given values of f(-2) = a and f(6) = b.
First, let's find the equation with f(-2) = a. To get this equation, we substitute x = -2 into the remainder (x + 6):
(-2 + 6) = 4
So, the first equation is:
f(-2) = 4
Next, let's find the equation with f(6) = b. We substitute x = 6 into the remainder (x + 6):
(6 + 6) = 12
So, the second equation is:
f(6) = 12
Now that we have the two equations, we can solve them to find the values of a and b.
From the equation f(-2) = 4, we know that a = 4.
From the equation f(6) = 12, we know that b = 12.
Therefore, the value of b/a is:
b/a = 12/4 = 3
So, the value of b/a is 3.