Quadratic functions

[fiery123]

Can someone help me with this problem.
Consider a quadratic function f(x) = 3x^2 - 9x + 4 and f(a)=f(b), where 'a' does not equal to 'b'.
Find the value of a+b.

[Glaysher]

3x² - 9x + 4 = 3[x² - 3x] + 4

= 3(x - 3/2)² - 27/4 + 4

Minimum point at (1.5, -2.75)

So a and b do not equal 1.5

To get the same value when put into the function they must be an equal distance from 1.5

So assume a < 1.5 and b > 1.5

Then 1.5 - a = b - 1.5

a + b = 3

[fiery123]

ah thanks a lot for your help.