# Math Help - discriminant

1. ## discriminant

I know this sounds stupid but I actually need help with this!

in x² + x + 3

why is the discriminant always positive?

2. 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

3. 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.

4. That's why I'm stuck, the question paper definitely says its always positive

5. 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

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

7. 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.