Question

3. Find the condition that the roots of the equation a0x^3+3a1x^2+3a2x+a3=0 may be in AP.​

Answer 1

Step-by-step explanation:

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Answer 2

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Let the roots be p, q, r. The roots are in A.P. So,

2q = p +r,

3q=p+q+r.

Using theory of equations,

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-b a p+q+r=

-b 3a So, q

But, q is a root of the given equation. So aq³ +bq² + cq + d = 0,

a 3 ( 35 ) ² + b ( 35) ² 3a 3a -b 3a + c + d = 0,

Rearranging, we get

2b³ + 27a²d = 9abc.

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