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Math Help - Roots of Quadratic Equation

  1. #1
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    Roots of Quadratic Equation

    Which term describes the roots of the equation
    2x^2 + 3x - 1 = 0?
    (1) rational (3) equal
    (2) irrational (4) imaginary


    I guessed choice (2) and was right but I still do not know what makes the roots irrational in this case.
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  2. #2
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    The roots are found by the quadratic formula, x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}

    In your equation, a = 2, b = 3 and c = -1.

    So x = \frac{-3 \pm \sqrt{9 + 8}}{4} = \frac{-3 \pm \sqrt{17}}{4}

    This shows there are 2 real roots. Now 17 is a prime number - it can only be divided exactly by 1 and itself. The square root of any prime number is irrational - it cannot be expressed as a fraction. So the roots of the equation are therefore irrational.
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  3. #3
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    nice....

    Quote Originally Posted by nzmathman View Post
    The roots are found by the quadratic formula, x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}

    In your equation, a = 2, b = 3 and c = -1.

    So x = \frac{-3 \pm \sqrt{9 + 8}}{4} = \frac{-3 \pm \sqrt{17}}{4}

    This shows there are 2 real roots. Now 17 is a prime number - it can only be divided exactly by 1 and itself. The square root of any prime number is irrational - it cannot be expressed as a fraction. So the roots of the equation are therefore irrational.
    Very nicely explained.
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