discriminant

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October 14th 2007, 10:24 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, 10:26 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, 10:27 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, 10:48 AM
me2612

That's why I'm stuck, the question paper definitely says its always positive
October 14th 2007, 10:51 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, 09:04 AM
red_dog

The discriminant is negative, so the function $f(x)=x^2+x+3$ is always positive.
October 15th 2007, 09:27 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

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

The conclusion follows.

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