If root of the equation  a^{3}-12a^{2}+39a-28=0 are in A.P than its common difference is

  • Option 1)

    \pm 1

  • Option 2)

    \pm 2

  • Option 3)

    \pm 3

  • Option 4)

    \pm 4

 

Answers (1)

As we learnt in 

Sum of roots of cubic Equation -

\alpha +\beta +\gamma = \frac{-b}{c}

 

- wherein

ax^{3}+bx^{2}+cx+d= 0

is the cubic equation

 

 

Product of roots of cubic equation -

\alpha \beta \gamma = \frac{-d}{a}

- wherein

ax^{3}+bx^{2}+cx+d= 0

is the cubic equation

 

 a^{3}-12a^{3}+39a-28=0

Let the roots be

\\ \alpha -d,\alpha ,\alpha +d\\*3\alpha = 12= > \alpha = 4\\*and\, \, \alpha \left ( \alpha -d \right )\left ( \alpha +d \right )=28\\*4\left ( 4^{2}-d^{2} \right )=28\\*Here\, \, d^{2}=9\\*= > d=\pm 3


Option 1)

\pm 1

Incorrect

Option 2)

\pm 2

Incorrect

Option 3)

\pm 3

Correct

Option 4)

\pm 4

Incorrect

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