# discriminant

• October 14th 2007, 11:24 AM
me2612
discriminant
I know this sounds stupid but I actually need help with this!

in x² + x + 3

why is the discriminant always positive?
• October 14th 2007, 11:26 AM
Jhevon
Quote:

Originally Posted by me2612
I know this sounds stupid but I actually need help with this!

in x² + x + 3

why is the discriminant always positive?

who told you the discriminant was positive? it is negative here. this quadratic has no real roots
• October 14th 2007, 11:27 AM
lordofsheep
Quote:

Originally Posted by me2612
I know this sounds stupid but I actually need help with this!

in x² + x + 3

why is the discriminant always positive?

the discriminant is never positive since b^2-4ac is the formula for the discriminant you would get -11 which would mean that equation only has imaginary roots.
• October 14th 2007, 11:48 AM
me2612
That's why I'm stuck, the question paper definitely says its always positive
• October 14th 2007, 11:51 AM
Jhevon
Quote:

Originally Posted by me2612
That's why I'm stuck, the question paper definitely says its always positive

are you sure it is not something like $x^2 + x - 3$? or $-x^2 + x + 3$ otherwise, it's a typo
• October 15th 2007, 10:04 AM
red_dog
The discriminant is negative, so the function $f(x)=x^2+x+3$ is always positive.
• October 15th 2007, 10:27 AM
Krizalid
Quote:

Originally Posted by red_dog
The discriminant is negative, so the function $f(x)=x^2+x+3$ is always positive.

Here's a short proof

$x^2 + x + 3 = \frac{{\left( {x + 1} \right)^2 + x^2 + 5}}
{2}$

The conclusion follows.