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The roots of $−2x^2 + x + 4$ are $α$ and $β$. Suppose another quadratic, $px^2 + qx + r$, has roots $α +1/β$ and $β + 1/α$

What is the form of the new quadratic?

To solve this I got that $α+β=1/2$ and $αβ=-2$.

After doing so I end up with;

$q/p = -1/4$ and $r/p = -2$

However, Im not sure how to proceed and how to find out p? So I was wondering what I would do next.

Thank you.

user639649
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1 Answers1

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If a quadratic $ax^2+bx+c$ has roots $\alpha$ and $\beta$, then $p(ax^2+bx+c)$ also has the same roots irrespective of the non-zero value of $p$. Hence, you can take any value of $p$ of your choice in your problem and the roots will remain same.

Martund
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