Asked by Jayden Haddy
Prove that if p and q are rational and p is not equal to 0, the roots of the quadratic equations p x(square) + 2qx -p +2q = 0 are rational.
Answers
Answered by
Steve
the discriminant is
4q^2 - 4p(2q-p)
= 4q^2 - 8pq + 4p^2
= 4(q-p)^2
which is a perfect square. Consider that in the light of the quadratic formula, and the result is clear.
4q^2 - 4p(2q-p)
= 4q^2 - 8pq + 4p^2
= 4(q-p)^2
which is a perfect square. Consider that in the light of the quadratic formula, and the result is clear.
There are no AI answers yet. The ability to request AI answers is coming soon!
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.