Function negative for all values of x

[Lilkaze]

Homework Statement

Find the range of values of m for which the function 3x^2 -12x + m is negative for all values of x.

Homework Equations

Is it possible for the function to be negative ? If so, how ?

The Attempt at a Solution

I tried using b^2 - 4ac < 0 and the result is m > 12 . However when i tried substituting *13* as the value of m and *1* as the value of x, the result is a positive number.

 

[Defennder]

I don't think that any such value of m exists. Just picture this intuitively. What does the graph look like? Is it shaped like a smiley expression or sad expression? Moreover, even if the discriminant is less than zero it just means that the graph doesn't cut the x-axis. It doesn't mean that it is below the x-axis.

 

[Gib Z]

Defennder is correct: No such value of m exists. Complete the square, or just see that 3x^2 - 12x itself can be made as large as required to cancel out any value of m.