1. ## Find k

Find a number k such that 4 and 1 are the solutions
of x^2 - 5x + k = 0.

2. Originally Posted by sologuitar
Find a number k such that 4 and 1 are the solutions
of x^2 - 5x + k = 0.
sub in 4 or 1 for x and solve for k

3. ## WOW!

Originally Posted by skeeter
sub in 4 or 1 for x and solve for k
I can't believe the problem is that easy.

4. It sure is! And I will confess that I would have suggested either

1) Use the quadratic formula: $\displaystyle x= \frac{5\pm\sqrt{25- 4k}}{2}$
and set $\displaystyle \frac{5+ \sqrt{25- 4k}}{2}= 4$ and $\displaystyle \frac{5- \sqrt{25- 4k}}{2}= 1$ and solve for k
or

2) Write $\displaystyle x^2- 5x+ k= (x- 1)(x- 4)$, multiply it out and solve for k.

But skeeter's suggestion is far simpler than either of those.

5. ## Thanks...

Originally Posted by HallsofIvy
It sure is! And I will confess that I would have suggested either

1) Use the quadratic formula: $\displaystyle x= \frac{5\pm\sqrt{25- 4k}}{2}$
and set $\displaystyle \frac{5+ \sqrt{25- 4k}}{2}= 4$ and $\displaystyle \frac{5- \sqrt{25- 4k}}{2}= 1$ and solve for k
or

2) Write $\displaystyle x^2- 5x+ k= (x- 1)(x- 4)$, multiply it out and solve for k.

But skeeter's suggestion is far simpler than either of those.
Thank you for the different methods.

6. The really nice thing is that all three methods give the same answer!