Solve for x

[curicuri]

First time on this forum, so let me know if my question should be put somewhere else on the forum!
Regarding the quadric equation (x^2+px+q)
If you have a function with no q such as x^2 + 2x. Could you consider q=0 so that the quadric equation can be used or do q has to have value bigger or smaller than 0. ??

Thank you for your time!

 

[Otis]

... Regarding the quadric equation (x^2+px+q) ...

Hello! First, some notes about notation. 'Quadric' refers to some surfaces (those functions have more than one variable). The expression above is 'quadratic' (i.e., a second-degree polynomial with one variable).

Also, it's not an equation. All equations contain an equals sign. The quadratic equation is:

y = x^2 + px + q

If you have a function with no q such as x^2 + 2x, [then could] you consider q=0 ... so that the quadric equation can be used ...?

Yes, q may be any Real number, including zero.

I assume you meant, "the quadratic formula can be used".

When the constant term in a quadratic polynomial is zero, we can find the roots also by factoring.

0 = x^2 + 2x

0 = x(x + 2)

The Zero-Product Property lets us write:

x = 0 \(\;\) OR \(\;\) x + 2 = 0

Cheers

?

 

[Harry_the_cat]

The quadratic formula can still be used if q=0. However it is much easier to solve using the method shown above by Otis.

 

[curicuri]

Thank you so much for precise and quick answers