# Function negative for all values of x

• Jun 14th 2008, 04:54 AM
Lilkaze
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.
• Jun 14th 2008, 05:01 AM
mr fantastic
Quote:

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.
• Jun 14th 2008, 05:06 AM
Moo
The rules are this way :

ax²+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 $x_1$ and $x_2$
$P(x)=a(x-x_1)(x-x_2)$

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