# Thread: Function negative for all values of x

1. ## Function negative for all values of x

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

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

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

Is it possible for the function to be negative ? Mr F says: Yes, but not for all values of x.

If so, how ?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.
Since the coefficient of x^2 is positive, it's impossible for this parabola to be negative for all values of x.

3. The rules are this way :

ax˛+bx+c

If the discriminant is strictly negative
The trinomial is of the same sign as a.

If the discriminant is equal to 0
Then it's a multiple of a perfect square and the sign is the sign of a.

If the discriminant is positive
There are 2 real roots $\displaystyle x_1$ and $\displaystyle x_2$
$\displaystyle P(x)=a(x-x_1)(x-x_2)$

And the sign of the trinomial is as following :
- sign of a in $\displaystyle ]-\infty ~,~x_1] \cup [x_2 ~,~+\infty[$
- inverse sign of a in $\displaystyle [x_1 ~,~ x_2]$