SOLUTION: Dear Sir/ Madam, Good day! kindly help me in answering this mathematical problem: Prove that if roots of ax^2+bx+c=0 are reciprocals, then a=c Thank you very much for your help

Question 766202: Dear Sir/ Madam,
Good day! kindly help me in answering this mathematical problem:
Prove that if roots of ax^2+bx+c=0 are reciprocals, then a=c
Thank you very much for your help!
Found 2 solutions by ramkikk66, MathTherapy:
Answer by ramkikk66(644) (Show Source): You can put this solution on YOUR website!
The roots of the quadratic equation a*x^2 + b^x + c = 0 are
1)
and
2)
If they are reciprocals of each other

Cross multiplying:

Dividing both sides by 4*a
We can do because we know that a cannot be 0 for a quadratic)

Hope you got it. Let me know if it is not clear :)

Answer by MathTherapy(10551) (Show Source): You can put this solution on YOUR website!

Dear Sir/ Madam,
Good day! kindly help me in answering this mathematical problem:
Prove that if roots of ax^2+bx+c=0 are reciprocals, then a=c
Thank you very much for your help!

Let root 1 = . Since the roots are reciprocals, then root 2 =
Product of roots: . Product of roots, based on the fact that they are reciprocals: , or 1

Therefore,

------ Cross-multiplying
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