Question

solve the equation 6x3-11x2+6x-1=0 given that the roots are HP​

Answer 1

Answer:

roots are : 1, 1/2 & 1/3

Step-by-step explanation:

roots : a, b, c

then....

a + b + c = 11/6

ab + bc + ca = 1

abc = 1/6

since....a, b, c are in HP

we have....1/a, 1/b, 1/c are in AP

hence....

1/a + 1/c = 2/b

now......

1/abc { ab + bc + ca } = 1/(1/6)

= 1/c + 1/a + 1/b = 6

= 2/b + 1/b = 6

= 3/b = 6

b = 1/2

now...

a + b + c = 11/6

a + c = 11/6 -1/2 = 4/3......(1)

and...

abc = 1/6

ac(1/2) = 1/6

ac = 1/3...(2)

from (1) & (2)...

a = 1 & c = 1/3

hence the roots are...1, 1/2, 1/3