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

let one root ß so, another is 6ß

equation ,
kx^2 -14x +8 =0

sum of roots = - coefficient of x /coefficient of x^2

ß + 6ß = 14/k

7ß =14/k

ß =2/k -----------(1)

product of roots = constant / coefficient of x ^ 2

ß × 6ß = 8/k

6ß^2 =8/k -------------(2)

divide equation (1) ÷ (2)

ß/6ß^2 =2/k × k/8

1/6ß =1/4

ß =2/3

put ß =2/3 in equation (1)
2/3=2/k

k =3