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. $\frac{9}{16}$
• B. $\frac{3}{16}$
• C. $\frac{3}{4}$
• D. $\frac{\sqrt{3}}{16}$

Answer 1

The correct option is B $\frac{3}{16}$

$4x^2-\sqrt{3}x-5=0$

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

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

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

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