If $$x_1, x_2$$ are two real roots of the quadratic equation $$x^2-mx+m-2=0$$, then what statement is correct about $$m$$ to hold the equation $$\dfrac{1}{x_1}+\dfrac{1}{x_2}=0$$ true?

Question

Uniteasy Admin · Accepted Answer

Reduce to the common denominator. The expression is transformed to
$$\dfrac{1}{x_1}+\dfrac{1}{x_2}$$ 
$$=\dfrac{x_1+x_2}{x_1x_2} $$
Since $$x_1, x_2$$ are two real roots of the quadratic equation $$x^2-mx+m-2=0$$, the sum of $$x_1+x_2$$ is concluded to be equal to $$m$$ by using Vieta's formula.
Therefore, $$\dfrac{1}{x_1}+\dfrac{1}{x_2}=0$$ if $$m=0$$
Choice A is correct

Multiple Choice Question (MCQ)

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