Home
Class 12
MATHS
If the roots of the cubic equation x^(3...

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

Text Solution

AI Generated Solution

To solve the problem, we need to find one of the roots and the value of \( a \) for the cubic equation \( x^3 - 9x^2 + a = 0 \) given that the roots are in Arithmetic Progression (A.P.). ### Step-by-Step Solution: **Step 1: Define the Roots** Let the roots of the cubic equation be \( \alpha - b \), \( \alpha \), and \( \alpha + b \). Since they are in A.P., the middle root is \( \alpha \) and the other two roots are symmetric around it. **Step 2: Use the Sum of Roots Formula** ...
Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBERS AND QUADRATIC EQUATIONS

    AAKASH INSTITUTE ENGLISH|Exercise Try Yourself|60 Videos

  • COMPLEX NUMBERS AND QUADRATIC EQUATIONS

    AAKASH INSTITUTE ENGLISH|Exercise Assignment (Section -A) (objective Type Questions ( one option is correct)|47 Videos

  • BINOMIAL THEOREM

    AAKASH INSTITUTE ENGLISH|Exercise Assignment (section-J) Objective type question (Aakash Challengers Questions)|4 Videos

  • CONIC SECTIONS

    AAKASH INSTITUTE ENGLISH|Exercise SECTION - J ( Aakash Challengers Questions )|16 Videos

Similar Questions

Explore conceptually related problems

If the roots of the equation x^(3) - px^(2) + qx - r = 0 are in A.P., then

Find the roots of the equation 3x^2+6x+3=0

If the roots of the equation x^3 -9x^2 + 23x-15=0 are in A.P then common difference of that A.P is

If the roots of the equation x^(3) - px^(2) + qx - r = 0 are in A.P., then prove that, 2p^3 −9pq+27r=0

Find the roots of the equations. Q. 2x^(2)+x-3=0

If the roots of the equation x^3-12x^2 +39x -28 =0 are in AP, then their common difference is

If the roots of the equation x^3-12x^2 +39x -28 =0 are in AP, then their common difference is

If alpha, beta, gamma are the roots of the cubic equation x^(3)+qx+r=0 then the find equation whose roots are (alpha-beta)^(2),(beta-gamma)^(2),(gamma-alpha)^(2) .

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

If (1+alpha)/(1-alpha),(1+beta)/(1-beta), (1+gamma)/(1-gamma) are the cubic equation f(x) = 0 where alpha,beta,gamma are the roots of the cubic equation 3x^3 - 2x + 5 =0 , then the number of negative real roots of the equation f(x) = 0 is :