Find the value of k for which one root of the quadratic equation kx2 14x 8 = 0 is 6 times the other

k = 3.

Step-by-step explanation:

If the 2 roots are A and B we have the relations:

AB = 8/k and A+B = -14/k.

We are given that A = 6B so

6B^2 = 8/k

B^2 = 8/6k = 4/3k

B = 2 /√(3k) (1)

Now A + B = -14/k so

6B + B = 7B = -14/k

B = -2/k(2)

Eliminating B from equations (1) and (2):

2 /√(3k) = -2/k

Cross multiply:

2k = -2√(3k)

Squaring both sides:

4k^2 = 4 * 3k

4k^2 = 12k

k^2 = 3k

k = 3.

the ratio of white tiles to blue tiles is 48: 16. the ratio in it's simplest form is 3: 1.

step-by-step explanation:

ratio: take the first number and add a colon next to it, then add the second number after that. make sure the ratio order matches up with the written problem!

simplest form: we can simplify the ratio 48 : 16 by dividing both terms by the greatest common factor (gcf).

the gcf of 48 and 16 is 16.

divide both terms by 16:

48 ÷ 16 = 3

16 ÷ 16 = 1

reducing to simplest form:

48 : 16 = 3 : 1