(x^2-x)^2+5(x^2-x) +4=0

Asked by shruthinair5848.10sdatl | 19th Jun, 2020, 10:12: AM

Expert Answer:

This question can be solved using quadratic equation by making certain substitution.
Take x2 - x = y, we have
y2 + 5y + 4 = 0
Solving this using factorisatin method
y2 + 4y + y + 4 = 0
y(y + 4) + y + 4 = 0
(y + 4)(y + 1) = 0
y = -4 or y = -1
Using y = x2 - x, we have
x2 - x + 4 = 0 or x2 - x + 1 = 0
Using quadratic formula here because there does not exist any real numbers whose addition -1 and product is 4
 
straight x space equals space fraction numerator negative left parenthesis negative 1 right parenthesis plus-or-minus square root of left parenthesis negative 1 right parenthesis squared minus 4 left parenthesis 1 right parenthesis left parenthesis 4 right parenthesis end root over denominator 2 left parenthesis 1 right parenthesis end fraction space space or space space fraction numerator negative left parenthesis negative 1 right parenthesis plus-or-minus square root of left parenthesis negative 1 right parenthesis squared minus 4 left parenthesis 1 right parenthesis left parenthesis 1 right parenthesis end root over denominator 2 left parenthesis 1 right parenthesis end fraction
straight x space equals space fraction numerator 1 plus-or-minus square root of negative 15 end root over denominator 2 end fraction space space or space space straight x space equals space fraction numerator 1 plus-or-minus square root of negative 3 end root over denominator 2 end fraction
Since space square space root space of space straight a space negative space number space is space not space defined space
straight i. straight e. space In space both space the space cases space the space discriminant space straight i. straight e. space straight b squared minus 4 ac space less than space 0
Therefore comma space the space roots space are space not space real.
Hence comma space there space are space no space real space roots space exist space for space the space given space quadratic space equation.

Answered by Renu Varma | 19th Jun, 2020, 02:43: PM