SOLUTION: How many real zeroes are there in f(x) = (x + 3)(x – 4)(x + 6)(x^2 + 7)? @ This is fairly straightforward. Only the last factor results in imaginary solutions a. 3 b. 5 c.

Algebra ->  Equations -> SOLUTION: How many real zeroes are there in f(x) = (x + 3)(x – 4)(x + 6)(x^2 + 7)? @ This is fairly straightforward. Only the last factor results in imaginary solutions a. 3 b. 5 c.      Log On


   

Question 152515: How many real zeroes are there in f(x) = (x + 3)(x – 4)(x + 6)(x^2 + 7)?
@ This is fairly straightforward. Only the last factor results in imaginary solutions
a. 3
b. 5
c. 4
d. None of the above

Answer by mducky2(62) About Me  (Show Source):
You can put this solution on YOUR website!

Let's find the zeroes of the function. Don't be fooled by the terminology. A zero of the function merely means any value of x that makes f(x) = 0. If any of the factors are zero, f(x) would equal zero. Therefore, we should individually solve for x with each factor equated to zero.

x+%2B+3+=+0
x+=+-3
Since x is a real number, this looks like a real zero.

x+-+4+=+0
x+=+4
Since x is a real number, this also looks like a real zero.

x+%2B+6+=+0
x+=+-6
Since x is a real number, this still looks like a real zero.

x%5E2+%2B+7+=+0
x%5E2+=+-7
x+=+sqrt%28-7%29
Any square root of a negative number will not be a real number, so this is not a real zero.

It looks like there are 3 total zeroes. We know there can't be any more because we have equated every possible factor of the function with zero. Therefore, the answer is a.