Find All Values of k for Equal Roots in x^2-kx+4=0

[priscilla98]

Homework Statement

Use the disciminant to determine all values of k that would result in the equation x^2 - kx + 4 = 0 having equal roots.

Homework Equations

x = -b +/- (square root) b^2 - 4ac and divide by 2a

or b^2 - 4ac

The Attempt at a Solution

a = 1
b = - 1
c = 4

I'm a little confused with this problem because instead of a number by b there's a k.

 

[HallsofIvy]

Homework Statement

Use the disciminant to determine all values of k that would result in the equation x^2 - kx + 4 = 0 having equal roots.

Homework Equations

x = -b +/- (square root) b^2 - 4ac and divide by 2a

or b^2 - 4ac

The Attempt at a Solution

a = 1
b = - 1
c = 4

I'm a little confused with this problem because instead of a number by b there's a k.

Which means b is NOT "-1", it is "-k". (That's the whole point of algebra isn't it- that numbers are represented by letters?) The discriminant is, as you say $b^2- 4ac$ which, here, is [itex](-k)^2- 4(1)(4)= k^2- 16[/math].

Now, in order to have equal roots, what must be true of the discriminant? What values of k make that true?

 

[priscilla98]

Thanks, i understand now. Therefore, you would have to factor k^2 - 16, (k +4)(k-4), thanks a lot