Please send the complete solution step by step.

Asked by sudhanshubhushanroy | 20th Nov, 2017, 08:24: AM

Expert Answer:

begin mathsize 16px style Given space equation space is space open parentheses ax squared plus straight c close parentheses straight y plus open parentheses straight a apostrophe straight x squared plus straight c apostrophe close parentheses equals 0
ax squared straight y plus cy plus straight a apostrophe straight x squared plus straight c apostrophe equals 0
straight x squared open parentheses ay plus straight a apostrophe close parentheses plus cy plus straight c apostrophe equals 0
According space to space the space question space straight x space is space rational.
rightwards double arrow Discriminant space should space be space straight a space perfect space square.
rightwards double arrow Discriminant space equals space 0 squared minus 4 open parentheses ay plus straight a apostrophe close parentheses open parentheses cy plus straight c apostrophe close parentheses
rightwards double arrow Discriminant space equals minus 4 open parentheses acy squared plus ac apostrophe straight y plus straight a apostrophe cy plus straight a apostrophe straight c apostrophe close parentheses
Given space that space ac space is space negative.
rightwards double arrow negative ac space is space positive.
rightwards double arrow Discriminant space equals minus 4 open parentheses ac apostrophe minus straight a apostrophe straight c close parentheses squared
rightwards double arrow Discriminant space equals 0
rightwards double arrow negative 4 open parentheses ac apostrophe minus straight a apostrophe straight c close parentheses squared equals 0
rightwards double arrow ac apostrophe minus straight a apostrophe straight c equals 0
rightwards double arrow fraction numerator straight a over denominator straight a apostrophe end fraction equals fraction numerator straight c over denominator straight c apostrophe end fraction

Given space that space ac space is space negative.
rightwards double arrow negative ac space is space positive.
end style

Answered by Sneha shidid | 1st Dec, 2017, 05:36: PM

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