Value of k when there are two equal roots

[veronicadeno]

I'm studying for an Advanced Math 12 Regional Exam and got the following multiple choice question wrong.

If the equation 2kx^2-4x+1=0 has two equal roots (double root), then the value of k is ___.

The correct answer is k=2, but I don't understand why. Can someone explain it to me?

 

[pka]

I'm studying for an Advanced Math 12 Regional Exam and got the following multiple choice question wrong.
If the equation 2kx^2-4x+1=0 has two equal roots (double root), then the value of k is ___.
The correct answer is k=0, but I don't understand why. Can someone explain it to me?

The correct answer is not \(\displaystyle k=0 \)
The correct answer occurs when discriminant is zero: \(\displaystyle b^2-4ac=0 \)

So \(\displaystyle (-4)^2-4(2k)(1)=0 \) thus \(\displaystyle k=~? \)

 

[veronicadeno]

The correct answer is not \(\displaystyle k=0 \)
The correct answer occurs when discriminant is zero: \(\displaystyle b^2-4ac=0 \)

So \(\displaystyle (-4)^2-4(2k)(1)=0 \) thus \(\displaystyle k=~? \)

Re-checked the answer key, the answer should be k=2. My bad!

Okay, so
(-4)²-4(2k)(1)=0
16-8k=0
-8k=-16
k=2

Thanks!