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Math Help - Pre-calc question

  1. #1
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    Pre-calc question

    This is probably something really simple and i'm just a moron but I have a problem on my homework that says "write a standerd form equation if it passes through the point (-1,24) and has roots of x=3 and x=-i(square root of)(5)". If anyone could help me out and point me in the right dierection it would be much appreciated .
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  2. #2
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    Re: Pre-calc question

    I am not sure what's meant by "standard form equation" but I expect it means a polynomial with real coefficients. Remember that all nonreal roots appear as complex conjugates when this is the case. So

    \displaystyle \begin{align*} y &= a \left( x - 3 \right) \left[ x - \left( -i\sqrt{5} \right) \right] \left( x - i\sqrt{5} \right) \\ y &= a \left( x - 3 \right) \left( x^2 + 5 \right)   \end{align*}

    will suffice. Use the point that lies on the curve to evaluate \displaystyle \begin{align*} a \end{align*}.
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