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Q.

If ∝ is the only real root of the equation x3+bx2+cx+1=0(b

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answer is -1.57.

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Detailed Solution

At x=-1, the expression x3+bx2+cx+1=b-c<0  ∵b0 ⇒the equation x3+bx2+cx+1==0 must have a real root between -1 and 0 ⇒the only real root α of the equation must lie between -1 and 0 ⇒α<0 ⇒tan-11α=-π+cot-1α ∴tan-1α+tan-11α=tan-1α-π+cot-1α                                       =-π+π2                                        =-π2                                         = -1.57
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