Question

9. Given one of the root of the quadratic equation x^2 - 5kx+ k=0 is four times the other root, find the value of k

Answer 1

Answer:

k = 1/4.

Step-by-step explanation:

Let the roots be  r and 4r   and using the fact that sum of the roots = -b/a and product = a/c, we have:

r + 4r = -(-5k)

r*4r = k

5r = 5k

4r^2 = k

From the 3rd equation:

r = k, therefore:

4k^2 = k

4k = 1

k = 1/4.

Answer 2

Answer:

k=1/4

Step-by-step explanation:

x² - 5kx+ k=0  ....(1)

suppose 2 roots: a and 4a

(x-a)(x-4a)=0

x² - 5ax + 4a² = 0 ....(2)

compare (1) and (2): -5a = -5k              a=k

4a² = k                4a² = a   (substitute)

a(4a-1) = 0

a = 0 or a = 1/4        (if a=0   k=0 and x=0 is not the solution)

a = 1/4      k = 1/4

(a₂ = 1/4 * 4 = 1)