Question

How do you find the zeroes for `f(x) = x^2 – 9x – 70`?

Answer 1

`x=-14` and `x=5`

Explanation:

We need to think of two numbers, that, when I add them, sum up to `-9`, and when I multiply them, have a product of `-70`. Since the product is negative, we know the signs must be different.

Through some thought, we arrive at `-14` and `5` as our two numbers, because

`-14+5=-9` and

`-14*5=-70`

Thus, our equation is as follows:

`(x-14)(x+5)=0`

To find the zeroes, we take the opposite signs to get

`x=14` and `x=-5`

Hope this helps!

Answer 2

-5 and 14

Explanation:

`f(x) = x^2 - 9x - 70 = 0`
To solve f(x), find 2 numbers (real roots) knowing the sum (-b = 9) and the product (c = - 70). They are: - 5 and 14.

Note . This method avoids proceeding the lengthy factoring by grouping and solving the 2 binomials.