Mark the correct alternative in each of the following:

In a triangle ABC, a = 4, b = 3, $∠ A = 60 °$ then c is a root of the equation

(a) $c^{2} - 3 c - 7 = 0$ (b) $c^{2} + 3 c + 7 = 0$ (c) $c^{2} - 3 c + 7 = 0$ (d) $c^{2} + 3 c - 7 = 0$

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Solution

It is given that a = 4, b = 3 and $∠ A = 60 °$ .

Using cosine rule, we have

$\cos A = \frac{b^{2} + c^{2} - a^{2}}{2 b c} \Rightarrow \cos 60 ° = \frac{9 + c^{2} - 16}{2 \times 3 \times c} \Rightarrow \frac{1}{2} = \frac{c^{2} - 7}{6 c} \Rightarrow c^{2} - 7 = 3 c \Rightarrow c^{2} - 3 c - 7 = 0$

Thus, c is the root of $c^{2} - 3 c - 7 = 0$ .

Hence, the correct answer is option (a).

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