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  • Find the roots of the following quadratic equations, if they exist, by the method of completing the square: 4x ^2 + 3 root 3 x + 3 = 0

Q1.    Find the roots of the following quadratic equations, if they exist, by the method of completing the square:

                (iii)    4x^2 + 4\sqrt3 + 3 = 0

Answers (1)

best_answer

Given equation: 4x^2 + 4\sqrt3 + 3 = 0

On dividing both sides of the equation by 4, we obtain

\Rightarrow x^2+\sqrt3x+\frac{3}{4} = 0

Adding and subtracting  (\frac{\sqrt3}{2})^2  in the equation, we get

\Rightarrow (x+\frac{\sqrt3}{2})^2 +\frac{3}{4} - (\frac{\sqrt3}{2})^2 = 0

\Rightarrow (x+\frac{\sqrt3}{2})^2 = \frac{3}{4} - \frac{3}{4} = 0

\Rightarrow (x+\frac{\sqrt3}{2}) = 0\ or\ (x+\frac{\sqrt3}{2}) = 0

Hence there are the same roots and equal:

\Rightarrow x = \frac{-\sqrt3}{2}\ or\ \frac{-\sqrt3}{2}

Posted by

Divya Prakash Singh

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