Question

Find the value of k, for which one root of the quadratic equation kx2 – 14x + 8 = 0 is six times the other.

Answer 1

Hey mate..

here is your answer

Let roots of the equation are be a and b.

Given a = 6b

now, if a and b are roots then equation is

(x -a)(x -b) =0

=> x² - (a+b)x + ab =0

Now put a = 6b then

x² - (6b +b)x + 6b×b =0

=> x² - 7bx +6b² =0 ...............1

Given equation is

kx² -14x +8 =0

=> kx² - (14/k*x +(8/k) =0 .......................2

Compare equation 1 and 2, we get

7b =14/k

=> b= 14/(7*k)

=> b =2/k

=> b² = 4/k²...............3

and 6b² =8/k

=> 6b² =8/(6k)

=> b² =4/(3k) ...............4

Put value of b² in equation4, we get

4/k² = 4/(3k)

=>1/k = 1/3

=> k =3

So value of k is 3

hope it helps you!!!

please mark my answers as the brainliest answer.

Answer 2

Step-by-step explanation:

k=3

thank you for your time