Home
Class 12
MATHS
Given that the roots of the equation 24...

Given that the roots of the equation ` 24x^(3) - 26x^(2) + 9x - 1 = 0` are in HP , find them

Text Solution

Verified by Experts

Equation ` 24 x^(3) - 26x^(2) + 9x - 1 = 0 ` has its roots in H.P.
Let ` x = (1)/(y)`
` rArr (24)/(y^(3)) - (26)/(y^(2)) + (9) /(y) -1 = 0 `
` y^(3) - 9y^(2) + 26y - 24 = 0 ` has its roots in A.P.
Let the roots be
` alpha = a - d , beta = a , gamma = a+ d `
` alpha + beta + gamma = 3a = 9`
` rArr a = 3 `
` alpha beta gamma = a (a^(2) - d^(2)) = 24`
` rArr a^(2) - d^(2) = 8`
` rArr d^(2) = 1`
`rArr d = pm 1`
` alpha = 2 , beta = 3 , gamma = 4 `
`rArr ` Roots of original equation are `(1)/(2), (1)/(3), (1),(4)`
Promotional Banner

Topper's Solved these Questions

  • SEQUENCES AND SERIES

    AAKASH INSTITUTE|Exercise Try Yourself|85 Videos

  • SEQUENCES AND SERIES

    AAKASH INSTITUTE|Exercise Assignment (SECTION - A) One option is correct|60 Videos

  • RELATIONS AND FUNCTIONS

    AAKASH INSTITUTE|Exercise Assignment (Section - J) Aakash Challengers Questions|8 Videos

  • SETS

    AAKASH INSTITUTE|Exercise SECTION-I(Aakash Challengers Questions)|5 Videos

Similar Questions

Explore conceptually related problems

Find the roots of the equation 2x^(2)-9x-18=0

If the roots of the equation x^(3) + bx^(2) + 3x - 1 = 0 form a non-decreasing H.P., then

Roots of the equation 16 x ^(2) - 24 x + 9 =0 are

If alpha, beta and gamma are the roots of the equation x^(3) + 3x^(2) - 24x + 1 = 0 thebn find the value of (3sqrt(alpha)+3sqrt(beta)+ 3sqrt(gamma)).

The root of the equation 3^(2x)-10.3^(x)+9=0 are

Roots of equation x^(4)-10x^(3)+26x^(2)-10x+1=0 are

If the roots of the cubic equation x^(3) -9x^(2) +a=0 are in A.P., Then find one of roots and a

The roots of the equation 2^(x+2).3^((3x)/(x-1))=9 are given by

Roots of equation x^(5)-5x^(4)+9x^(3)-9x^(2)+5x-1=0 are

Find the roots of the following equations : x - (1)/(x) = 3, x != 0