Question

Solve for x by completing the square method:
$4x^2+11abx+6a^2{b}^2$ =0

• A. (-2ab)/3, -3ab
• B. (-3ab)/4, -2ab
• C. (-3ab)/4, -ab
• D. (-2ab)/3, -ab

Answer 1

The correct option is B (-3ab)/4, -2ab

$4x^2+11abx+6a^2{b}^2=0$

$\frac{4x^2+11abx+6a^2{b}^2}{4}=\frac{0}{4}$

$\Rightarrow x^2+\frac{11}{4}abx+\frac{6}{4}{a}^2{b}^2=0$

$\Rightarrow x^2+2.\frac{11}{2.4}abx+\frac{6a^2{b}^2}{4}=0$

$\Rightarrow x^2+2\times \frac{11}{8}abx+\frac{6a^2{b}^2}{4}=0$

$(x+\frac{11ab}{8}{)}^2=\frac{121a^2{b}^2}{64}-\frac{6a^2{b}^2}{4}$

$(x+\frac{11ab}{8}{)}^2=\frac{121a^2{b}^2-96a^2{b}^2}{64}=\frac{25a^2{b}^2}{64}$

$\Rightarrow x+\frac{11ab}{8}=\pm \sqrt{\frac{25a^2{b}^2}{64}}\Rightarrow x+\frac{11ab}{8}=\pm \frac{5ab}{8}$
$\Rightarrow x=\frac{-11ab}{8}\pm \frac{5ab}{8}$
$\Rightarrow x=\frac{-11ab+5ab}{8}=\frac{-6ab}{8}=\frac{-3ab}{4}$
or $\Rightarrow x=\frac{-11ab-5ab}{8}=\frac{-16ab}{8}=-2ab$
Hence, b is the correct option.