$T = ax^2+ bx+c$ $\Delta = b^2 - 4ac$ ------------------------------- Si $\Delta\lt 0$: $T$ a le sign of $a$ ------------------------------- Si $\Delta = 0$: $T$ has the sign of $a$, if $x$ is not equal to the root $x_0$ $T = 0$, if $x$ is equal to the root $x_0$ ------------------------------- If $\Delta \gt 0$: $T = 0$, if $x$ is equal to the roots $x_1$ or $x_2$ $T$ has the sign of $a$, if $x$ is outside the roots $x_1$ and $x_2$ $T$ has the sign of $-a$, if $x$ is between the roots $x_1$ and $x_2$ -------------------------------

Got it !

## $T \lt 0$ ??

 $T = -3x^2 + 7x - 2$ $T = x^2 - 3x -10$ $T = 9x^2 -6x + 1$

 Sign of $T = x^2+2x-15$ for $x=3$ $T = 0$ $T = x^2-5x-4 \gt 0$ for $x\gt ?$ $x^2+7 \gt 3x$ for $x ?$