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Question
Mark the correct alternative in each of the following:
In a triangle ABC, a = 4, b = 3, \[\angle A = 60°\] then c is a root of the equation
Options
\[c^2 - 3c - 7 = 0\]
\[c^2 + 3c + 7 = 0\]
\[c^2 - 3c + 7 = 0\]
\[c^2 + 3c - 7 = 0\]
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Solution
It is given that a = 4, b = 3 and \[\angle A = 60°\] Using cosine rule, we have
\[\cos A = \frac{b^2 + c^2 - a^2}{2bc}\]
\[ \Rightarrow \cos60° = \frac{9 + c^2 - 16}{2 \times 3 \times c}\]
\[ \Rightarrow \frac{1}{2} = \frac{c^2 - 7}{6c}\]
\[ \Rightarrow c^2 - 7 = 3c\]
\[ \Rightarrow c^2 - 3c - 7 = 0\]
Thus, c is the root of \[c^2 - 3c - 7 = 0\] Hence, the correct answer is option (a).
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