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Nature of Roots

Identify the ...

Question

Identify the zero product equation.

x^{2} + 3 x - 1 = 12

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x^{3} - x^{2} = x

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(x - 3) (x + 2) = (x + 1)

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(x - 2) (x + \frac{2}{3}) = 0

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Solution

The correct options are
B $x^{3} - x^{2} = x$
D $(x - 2) (x + \frac{2}{3}) = 0$
$(x - 2) (x + \frac{2}{3}) = 0$ is a zero product equation.
Since the factors are equals to zero.

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$(i i) {lim}_{x \to 2^{-}} \frac{x - 3}{x^{2} - 4}$

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$(v) {lim}_{x \to 0^{+}} \frac{2}{x^{\frac{1}{5}}}$

$(v i) {lim}_{x \to \frac{π^{-}}{2}} t a n x$

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$(v i i i) {lim}_{x \to 0^{-}} \frac{x^{2} - 3 x + 2}{x^{3} - 2 x^{2}}$

$(i x) {lim}_{x \to - 2^{+}} \frac{x^{2} - 1}{2 x + 4}$

$(x) {lim}_{x \to 0^{+}} (2 - c o t x)$

$(x i) {lim}_{x \to 0^{-}} 1 + c o s e c x$

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