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Question

If α and β are the roots of the equation 6x2-5x+1=0, then the value of tan-1α+tan-1β is


A

0

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B

π4

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C

1

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D

π2

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Solution

The correct option is B

π4


Explanation for the correct option:

Step 1: Find the sum and product of the roots of the given quadratic equation.

We have given a quadratic equation 6x2-5x+1=0, whose roots are α and β.

α+β=-baα+β=-(-5)6α+β=56αβ=caαβ=16

Step 2: Find the value of tan-1(α)+tan-1(β)

so,

tan-1α+tan-1β=tan-1561-16{tan-1(α)+tan-1(β)=tan-1(α+β1-αβ)}=tan-15656=tan-11=π4

tan-1α+tan-1β=π4

Hence, the correct option is (B).


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