Anonymous
Anonymous asked in Science & MathematicsMathematics · 9 years ago

prove that no real value of k exists for the equation x^2-kx+2k-10=0 has equal roots.(has onlyone value for x)?

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  • Hemant
    Lv 7
    9 years ago
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    QE : 1x² + (-k)x + (2k-10) = 0

    ∴ a = 1, b = -k, c = 2k - 10 .......... (1)

    For equal roots, discriminant Δ = b² - 4ac = 0.

    ∴ from (1),

    ... (-k)² - 4(1)( 2k - 10 ) = 0

    ∴ 1k² - 8k + 20 = 0.

    For this k-equation, discr. = (-8)² - 4(1)(20) = -14 < 0

    ∴ there is NO REAL value of k. ........................................ Q.E.D.

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