If the given quadratic equation has two integral roots \alpha\

Hugh Walls

Hugh Walls

Answered question

2022-04-23

If the given quadratic equation has two integral roots α and β then find α+β and |αβ|
x2(α2+11)x9+154(α+β)+16=0.

Answer & Explanation

catcher1307ieh

catcher1307ieh

Beginner2022-04-24Added 15 answers

Your cubic formulation is incorrect. The correct cubic equation is
4x351x2+44x741=0
Unfortunately, I could not find a better way of solving this problem other than bruteforcing this cubic using the rational root theorem. 13 is the only real root of this cubic, which implies α=13. Substituting this, you can easily find that β=7, which means α+β=|α+β|=20
For a quick check, substitute α=13 and β=7 in the quadratic to get
x220x+91=0
which has roots 7 and 13, proving that our solution is correct.

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