# Determine the value of k for which the equation 4x^2+kx+4=0 has one root equal to double the other root. Let the value of one of the roots be R, the other root is 2R.

Now the quadratic equation can be derived by the following operation: (x - R)(x - 2R) = 0

=> x^2 - xR - 2xR + 2R^2 = 0

=> x^2 - 3xR + 2R^2 =...

Start your 48-hour free trial to unlock this answer and thousands more. Enjoy eNotes ad-free and cancel anytime.

Let the value of one of the roots be R, the other root is 2R.

Now the quadratic equation can be derived by the following operation: (x - R)(x - 2R) = 0

=> x^2 - xR - 2xR + 2R^2 = 0

=> x^2 - 3xR + 2R^2 = 0

This is equivalent to 4x^2 + kx + 4 = 0

Dividing this by 4

=> x^2 + (k/4)x + 1 = 0

Now equate the coefficients of the x^2 - 3xR + 2R^2 = 0 and x^2 + (k/4)x + 1 = 0

We get k/4 = -3R and 2R^2 = 1

2R^2 = 1

=> R^2 = 1/2

=> R = 1/ sqrt 2 or -1/ sqrt 2

substitute this in k/4 = -3R

=> k = -12*(1/sqrt 2) or k = 12/sqrt 2

=> k = 6 sqrt 2 or k = -6 sqrt 2

Therefore k can take the values k = 6 sqrt 2 and k= -6 sqrt 2

Approved by eNotes Editorial Team