Question
Download Solution PDFThe roots of the equation 7x2 - 6x + 1 = 0 are tan α and tan β, where 2α and 2β are the angles of a triangle. Which one of the following is correct?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFExplanation:
Given:
tanα and tanβ are roots of 7x2 – 6x + 1 = 0
Hence,
⇒ tanα + tanβ = 6/7...(1)
⇒ tanα.tanβ = 1/7...(2)
⇒ tan(α+β) =
⇒ α +β = 45°
⇒ 2α +2β = 90°
It means the third angle of a triangle is 90°.
Hence, the triangle is right-angled.
Since
⇒tanα - tanβ =
Also
⇒ tan(α -β) =
⇒ tan2(α -β) =
=
Thus 2α≠2β
∴ Option (c) is correct.
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