In a triangle ABC, a = 4, b = 3, =60^ then c is a root of the equ… - Vidyadip

MCQ

In a triangle ABC, a = 4, b = 3, $\angle\text{A}=60^{\circ}$ then c is a root of the equation:

✓
$\text{c}^2-3\text{c}-7=0$
B
$\text{c}^2+3\text{c}+7=0$
C
$\text{c}^2-3\text{c}+7=0$
D
$\text{c}^2+3\text{c}-7=0$

✓

Answer

Correct option: A.

$\text{c}^2-3\text{c}-7=0$

It is given that a = 4, b = 3 and $\angle\text{A}=60^{\circ}$
Using cosine rule, we have
$\cos\text{A}=\frac{\text{b}^2+\text{c}^2-\text{a}^2}{2\text{bc}}$
$\Rightarrow\cos60^{\circ}=\frac{9+\text{c}^2-16}{2\times3\times\text{c}}$
$\Rightarrow\frac{1}{2}=\frac{\text{c}^2-7}{6\text{c}}$
$\Rightarrow\text{c}^2-7=3\text{c}$
$\Rightarrow\text{c}^2-3\text{c}-7=0$
Thus, c is the root of $\text{c}^2-3\text{c}-7=0.$
Hence, the correct answer is option (a).

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