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Question

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


A
6,154
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B
6,163
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C
3,16
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D
163,6
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Solution

The correct option is C $$\cfrac{-16}{3},6$$
$$x^2-\dfrac{2}{3}x=32$$
$$\Rightarrow$$  $$3x^2-2x=96$$
$$\Rightarrow$$  $$3x^2-2x-96=0$$
$$\Rightarrow$$  $$3x^2-18x+16x-96=0$$
$$\Rightarrow$$  $$3x(x-6)+16(x-6)=0$$
$$\Rightarrow$$  $$(x-6)(3x+16)=0$$
$$\Rightarrow$$  $$x-6=0$$ and $$3x+16=0$$
$$\therefore$$  $$x=6$$ and $$x=\dfrac{-16}{3}$$

Mathematics

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