SOLUTION: What is the largest value of k such that the equation x2 � 5x + k has at least one real root?

Click here to see ALL problems on Quadratic Equations

Question 922555: What is the largest value of k such that the equation x2 � 5x + k has at least one real root?
Found 2 solutions by jim_thompson5910, josmiceli:
Answer by jim_thompson5910(35256) (Show Source):
You can put this solution on YOUR website!
is in the form where , ,

Plug in , ,

-------------------------------------------------------

We will have at least one real solution when

Plug in . Solve for k.

-------------------------------------------------------

The answer as a fraction is

The answer as a decimal is

If you insist on having k be a whole number, then round to the nearest whole number to get

In terms of a decimal, the largest k can be is 6.25 or 6 (depending on if you want a whole number or not).

------------------------------------------------------------------------

Let me know if that helps or not. Thanks.

If you need more help, feel free to email me at jim_thompson5910@hotmail.com

My Website: http://www.freewebs.com/jimthompson5910/home.html

Answer by josmiceli(19441) (Show Source):
You can put this solution on YOUR website!

The quadratic formula is:

The "discriminant" is:

For at least 1 real root,

-----------

----------------
check:
suppose

which means 1 real root
and if , there are 2 real roots