Question 152515
<br>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.
<br>{{{x + 3 = 0}}}
{{{x = -3}}}
Since x is a real number, this looks like a real zero.
<br>{{{x - 4 = 0}}}
{{{x = 4}}}
Since x is a real number, this also looks like a real zero.
<br>{{{x + 6 = 0}}}
{{{x = -6}}}
Since x is a real number, this still looks like a real zero.
<br>{{{x^2 + 7 = 0}}}
{{{x^2 = -7}}}
{{{x = sqrt(-7)}}}
Any square root of a negative number will not be a real number, so this is not a real zero.
<br>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.