Question

The expression x^2- x + 8.75 factors as (x + 2.5)(x - a) for some positive value "a". What is a?

step by step, please.

Answer 1

3.5

Explanation:

Write out quadratic

`{x}^(2) - x + 8.75`

We are given that x+2.5 is a factor.

So our roots look like

`(x + 2.5)(x - a)`

Let apply the foil method to find some missing parts.

`x * x = {x}^(2)`

`x * - a = - ax`

`2.5 * x = 2.5`

`2.5 * - a = - 2.5a`

We know that the outer terms must multiply to 8.75. We also know that the middle terms must add up to -1.

`- 2.5a = 8.75`

`2.5x - ax = -1`

The only number that satisfy this equation is

`- 3.5`

Since it already negative, it is

`3.5`