For what value of a does the equation ax^2−3x−5=0 have 1 as one of its roots?

First, rearrange the equation so you have just ax² on one side. This can be done by adding -3x and -5 on both sides of the equation:
ax²=3x+5
Now, substitute x for 1 and simplify:
a(1²)=(3×1)+5
1a=3+5
a=8
You can double check this by substituting a for 8 back into the original equation:
(8×1²)-(3×1)-5=0
8-3-5=0

The household makes $424.45