Question

find the value of k , for which one root of quadratic equation k$x^{2}$-14x+8=0 is six timesthe other

Answer 1

Let roots be a and b

Given, a = 6b 

if a and b are roots then equation will be (x -a)(x -b) =0

 (x -a)(x -b) =0

x^2 - (a+b)x + ab =0 

x^2 - (6b +b)x + 6b^2 =0

x^2- 7bx +6b^2 =0 

Given,  kx^2 -14x +8 =0

7b =14/kb =2/k 

b^2 = 4/k^2               ----------------- (i)

and 6b^2 =8/k

b^2 =4/3k                ----------------  (ii)

from (i) and(ii)

4/k^2 = 4/3k

k =3.


Hope this helps!