Let f(x) = 3x^2 – 2x + n and g(x) = mx^2 – nx + 2. The functions are combined to form the new

Question

Let f(x) = 3x^2 – 2x + n and g(x) = mx^2 – nx + 2. The functions are combined to form the new
functions h(x) = f(x) - g(x) and j(x) = f(x) + g(x). Point (6, 2) is in the function h(x), while the point
(-2, 10) is in the function j(x). Determine the exact values of m and n.

catharine · Accepted Answer

can you post a full solution?

oobleck · Answer

So, doing the combinations,
h(x) = ( 3x^2 – 2x + n)-(mx^2 – nx + 2) = (3-m)x^2 - (n+2)x + (n+2)
Since h(6) = 2, that gives
(3-m)*6^2 - (n+2)*6 + (n+2) = 2
36m+5n = -96

Now do the same with j(x). That will give you two equations to solve for m and n.