Multiple Choice Question (MCQ)

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?

  1. m=0

  2. ×

    m=2

  3. ×

    m=0 or m=2

  4. ×

    does not exist

Collected in the board: Vieta's Formula

Steven Zheng posted 1 hour ago

Answer

  1. 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

Steven Zheng posted 1 hour ago

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