Question

Write a quadratic equation in standard form that has two solutions, 6 and - 8

Answer 1

We want an equation which equals
0
at the given points
6
and
−
10
.
Our quadratic equation should be a product of expressions which are zero at the specified roots.
Consider
(
x
−
6
)
⋅
(
x
+
10
)
=
0
This equality holds if
x
=
6
since
(
6
−
6
)
⋅
(
6
+
10
)
=
0
⋅
16
=
0

And the equality holds if
x
=
−
10
since
(
−
10
−
6
)
⋅
(
−
10
+
10
)
=
−
16
⋅
0
=
0
Expanding this equation by the FOIL method, we get:
x
2
+
10
x
−
6
x
−
60
Combining like terms, we find our solution: