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Math Help - The roots of a quadratic equation

  1. #1
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    The roots of a quadratic equation

    Can anyone kindly help me with the following please?

    The roots of the equation x2 + 3x − 2 = 0 are α and β. Form a new equation with roots:

    (a) α - 1 and β + 2

    (b) α +2 and β + 1

    The sum of the new roots is easy but I am finding the product of the new roots difficult.

    Thanks in advance.
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  2. #2
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    Quote Originally Posted by yobacul View Post
    Can anyone kindly help me with the following please?

    The roots of the equation x2 + 3x − 2 = 0 are α and β. Form a new equation with roots:

    (a) α - 1 and β + 2

    (b) α +2 and β + 1

    The sum of the new roots is easy but I am finding the product of the new roots difficult.

    Thanks in advance.
    The roots are \alpha = \frac{-3 + \sqrt{17}}{2} and \beta = \frac{-3 - \sqrt{17}}{2}.

    Use these to calculate the required new roots. Now construct new quadratic equations form these roots.

    (a) \alpha - 1 = \frac{-5 + \sqrt{17}}{2} and \beta + 2 = \frac{1 - \sqrt{17}}{2}.

    So a new equation is \left( x + \frac{5 - \sqrt{17}}{2} \right) \cdot \left( x - \frac{1 - \sqrt{17}}{2}\right) = 0 \Rightarrow \, ....
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  3. #3
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    Exclamation The roots of a quadratic equation

    Thanks for your reply. However, the teacher told us that we have to find the new quadratic equation without solving the previous; in the sense that we are required to make use of the sum of roots and product of roots of the original equation.
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