Question

What are the zeros of the function f(x)=x^2-2x-15?

Answer 1

F(x) = x² - 2x - 15
x = -(-2) +/- √((-2)² - 4(1)(-15))
                        2(1)
x = 2 +/- √(4 + 60)
                 2
x = 2 +/- √(64)
             2
x = 2 +/- 8
           2
x = 1 + 4
x = 1 + 4      x = 1 - 4
x = 5            x = -3

Answer 2

To find the zeros of this function, we must first set the entire function equal to 0

f(x) = x² - 2x - 15 = 0

Since this is a quadratic function, we must use the quadratic formula, which is:

$\frac{-b +/- \sqrt{b^{2} - 4(a)(c) } }{2a}$

Let's assign a, b, and c using our first function
x² means a = 1 (because it could be written as 1x²)
-2x means b = -2
-15 means c = -15

Now let's plug those in:

$\frac{-(-2) +/- \sqrt{(-2)^{2} - 4(1)(-15) } }{2(1)}$

which simplifies to:

$\frac{2 +/- \sqrt{(4 + 60} }{2}$

Simplified further:

$\frac{2 +/- \sqrt{(64} }{2}$
$\frac{2 +/- 8 }{2}$
And divide it by the 2 on the bottom gives us:

$2 +/- 4$

2+4 = 6
2-4 = -2

So the zeros of this function are -2 and 6