Question

The roots of the equation $x^2-\frac{2}{3}x=32$ are

• A. $6,\frac{-15}{4}$
• B. $-6,\frac{-16}{3}$
• C. $3,16$
• D. $\frac{-16}{3},6$

Answer 1

Answer: (D)

$\frac{-16}{3},6$

$x^2-\frac{2}{3}x=32$

$\Rightarrow$ $3x^2-2x=96$

$\Rightarrow$ $3x^2-2x-96=0$

$\Rightarrow$ $3x^2-18x+16x-96=0$

$\Rightarrow$ $3x(x-6)+16(x-6)=0$

$\Rightarrow$ $(x-6)(3x+16)=0$

$\Rightarrow$ $x-6=0$ and $3x+16=0$

$\therefore$ $x=6$ and $x=\frac{-16}{3}$