Discriminant of quadratic equations

[Porty]

I know this is probably really easy, but i just can't figure it out..

Homework Statement

Find values of k for which (5 + 4x - x^2 = k) has equal roots.

I know the answer is k = 9 but i don't know how to get there..

Homework Equations

ax^2 + bx + c = 0
Discriminant = b^2 - 4ac

I know the discriminant has to equal 0 for the equation to have equal roots..

The Attempt at a Solution

But i get Discriminent = 36..?

and the roots equaling -1 or 5..?

Im lost.

 

[songoku]

I got k = 9, please show me your work so i can check it out

 

[HallsofIvy]

I know this is probably really easy, but i just can't figure it out..

Homework Statement

Find values of k for which (5 + 4x - x^2 = k) has equal roots.

I know the answer is k = 9 but i don't know how to get there..

Homework Equations

ax^2 + bx + c = 0
Discriminant = b^2 - 4ac

I know the discriminant has to equal 0 for the equation to have equal roots..

The Attempt at a Solution

But i get Discriminent = 36..?

and the roots equaling -1 or 5..?

Im lost.

Yes, x^2- 4x- 5= 0 has discrimant 36 and roots -1 and 5 but that is NOT the equation you want- you've dropped the "k" which is the whole point of this problem! In order to write 5 + 4x - x^2 = k as "ax^2+ bx+ c= 0", subtract k from both sides and write it as -x^2+ 4x+ 5-k= 0. Now a= -1, b= 4, and c= 5-k. The discriminant is b^2- 4ac= (4)^2- 4(-1)(5-k). Set that equal to 0 and solve for k.

 

[Porty]

HallsofIvy...

Yep yep that's it...

-x^2 + 4x + 5 - k = 0
= 4^2 - 4(-1)(5-k)
= 36 - 4k
4k = 36
k = 9

Now i can sleep... Thank you