Answer:
3.5
Step-by-step explanation:
Write out quadratic
[tex] {x}^{2} - x + 8.75[/tex]
We are given that x+2.5 is a factor.
So our roots look like
[tex](x + 2.5)(x - a)[/tex]
Let apply the foil method to find some missing parts.
[tex]x \times x = {x}^{2} [/tex]
[tex]x \times - a = - ax[/tex]
[tex]2.5 \times x = 2.5[/tex]
[tex]2.5 \times - a = - 2.5a[/tex]
We know that the outer terms must multiply to 8.75. We also know that the middle terms must add up to -1.
[tex] - 2.5a = 8.75[/tex]
[tex] 2.5x - ax = -1[/tex]
The only number that satisfy this equation is
[tex] - 3.5[/tex]
Since it already negative, it is
[tex]3.5[/tex]
