# Thread: Equations and range of values..

1. ## Equations and range of values..

Hi, thnx for help

How do i find the range of values of k for which the equation x^2+5x+k=0 (i dont know how to find values )

and also how to solve the equation 4x^2+20x+25=0 i tried to use the formula but i didnt get a answer that worked... thnx

2. Originally Posted by Chez_
Hi, thnx for help

How do i find the range of values of k for which the equation x^2+5x+k=0 (i dont know how to find values )

If $\displaystyle x^2 + 5x + k = 0$, we must have:

$\displaystyle x = \frac {-5 \pm \sqrt{25 - 4k}}2$

this of course, only has real solutions when we are withing the domain of the square root. thus we require $\displaystyle 25 - 4k \ge 0$. what is the range of $\displaystyle k$-values for which this happens?

and also how to solve the equation 4x^2+20x+25=0 i tried to use the formula but i didnt get a answer that worked... thnx
the quadratic formula can work, but it is overkill. this equation can be factored.

$\displaystyle 4x^2 + 20x + 25 = (2x + 5)(2x + 5) = (2x + 5)^2$

So, $\displaystyle 4x^2 + 20x + 25 = 0 \implies (2x + 5)^2 = 0$.

now continue