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!


Let root 1 = {{{r[1]}}}. Since the roots are reciprocals, then root 2 = {{{1/r[1
]}}}

Product of roots: {{{c/a}}}. Product of roots, based on the fact that they are reciprocals: {{{r[1]* (1/r[1])}}}, or 1


Therefore, {{{c/a = 1}}}


{{{highlight_green(c = a)}}} ------ Cross-multiplying