1. ## Discriminant

Find the smallest value of the interger $b$ for which $3x^2+bx+2$ is positive for all values of x.

My attempt

since its always postive,

$b^2-4ac<0$
$b^2-4(3)(2)<0$
$b^2-24<0$
$b^2<24$
$b<\sqrt{24}$

however, the answer is $-4$

2. Originally Posted by Punch
Find the smallest value of the interger $b$ for which $3x^2+bx+2$ is positive for all values of x.

My attempt

since its always postive,

$b^2-4ac<0$
$b^2-4(3)(2)<0$
$b^2-24<0$
$b^2<24$
$b<\sqrt{24}$

however, the answer is $-4$

Well...yes. you forgot that when taking square roots of real numbers we must deal with positive and/or negative values, so

$b^2<24\iff |b|<\sqrt{24}\iff -\sqrt{24} the minimal integer (as required) value b can take is $[-\sqrt{24}]+1=-4$ ...

Tonio

3. Hello, Punch!

And be sure to answer the question.

Find the smallest integer value of $b$ for which $3x^2+bx+2$ is positive for all values of $x.$

My attempt: . $b^2\:<\:24 \qquad{\color{blue}\Longrightarrow}\qquad {\color{blue}|b| \:<\:\sqrt{24}}$

However, the answer is $-4$

We have: . $-\sqrt{24} \:<\:b\:<\:\sqrt{24}$

. . . . . . . . $-4.9 \:<\:b\:<\:4.9$

So $b$ is between -4.9 and +4.9

Code:
          ↓
- - + o * * * * * * * * * * * * * * * * * o + - -
-5  -4  -3  -2  -1   0   1   2   3   4   5

So the least integer value of $b$ is -4.

Edit: ah, Tonio beat me to it . . . *sigh*
.

4. Thanks! you 2 are a great help heh!