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Question

Which constant should be added and subtracted to solve the quadratic equation $${ 4x }^{ 2 }-\sqrt { 3x } -5=0$$ by the method of completing the square ? 


A
916
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B
316
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C
34
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D
316
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Solution

The correct option is B $$\dfrac { 3 }{ 16 } $$
$$4x^2-\sqrt{3}x-5=0$$

$$\Rightarrow (2x)^2-\dfrac{\sqrt{3}}{2}2x-5=0$$

$$\Rightarrow (2x)^2-2\dfrac{\sqrt{3}}{4}2x+\left(\dfrac{\sqrt{3}}{4}\right)^2-\left(\dfrac{\sqrt{3}}{4}\right)^2-5=0$$

$$\Rightarrow \left(2x-\dfrac{\sqrt{3}}{4}\right)^2-\dfrac{3}{16}-5=0$$      ...{$$\because$$  We know, $$a^2-2ab+b^2=(a-b)^2$$}

Hence, we had to add $$\dfrac{3}{16}$$ to complete the square.

Maths

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