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  • Find the conditions, if the roots of the equation x3 - px2 + qx - r = 0 are in  AP?Option: 1 <img alt="2p^3 + 9p

Find the conditions, if the roots of the equation x3 - px2 + qx - r = 0 are in  AP?

Option: 1

2p^3 + 9pq - 27r = 0


Option: 2

2p^3 - 9pq + 27r = 0


Option: 3

4p^3 - 9pq + 27r = 0


Option: 4

4p^3 + 9pq - 27r = 0


Answers (1)

best_answer

let the roots be a-d, a and a+d, then: 

Sum of the roots = a-d + a + a+d = 3a = p ⇒ a = p/3

Since this value of a should satisfy the equation, so we put the value in equation and we get

 

\\\mathrm{\Rightarrow\left ( \frac{p}{3} \right )^3-p\left ( \frac{p}{3} \right )^2+q\frac{p}{3}-r=0} \\\mathrm{\Rightarrow p^3 - 3p^3+9pq-27r = 0} \\\mathrm{or \;2p^3 - 9pq + 27r = 0}

Correct option is (b)

Posted by

shivangi.bhatnagar

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