$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 !

> $\LARGE T \lt 0$ ??

> $\LARGE T = -3x^2 + 7x - 2$	$\LARGE T\lt 0$ if $\LARGE x\lt \frac{1}{3}$ and $\LARGE x\gt 2$
> $\LARGE T = x^2 - 3x -10$	$\LARGE T\lt 0$ if $\LARGE x\gt -2$ and $\LARGE x\lt 5$
> $\LARGE T = 9x^2 -6x + 1$	$\LARGE T\lt 0$ never

Answer

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