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Math Help - Showing that there are real roots.

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    Exclamation Showing that there are real roots.

    (p+1)x2+(2p+3)x+(p+2)=0Need help solving it and showing that the equation has real roots for all values of p. Explanation as well please. Thanks
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    Re: Showing that there are real roots.

    Quote Originally Posted by acedurza View Post
    (p+1)x2+(2p+3)x+(p+2)=0Need help solving it and showing that the equation has real roots for all values of p. Explanation as well please. Thanks
    I assume this is \displaystyle \begin{align*} \left( p + 1 \right) x^2 + \left( 2p + 3 \right)^2 x + \left( p + 2 \right) = 0 \end{align*}. This is a quadratic of the form \displaystyle \begin{align*} a\, x^2 + b\, x + c = 0 \end{align*}. These quadratics only have real solutions when the discriminant \displaystyle \begin{align*} \Delta = b^2 - 4ac \end{align*} is nonnegative. So start by evaluating the discriminant.
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