#QUADRATIC-1


Find the roots of the equation  x^4 - 10x^3 + 5x^2 + 100x + 100 = 0 ?

SOLUTION-
x^4 -10x^3 +5x^2 +100x +100 = 0
Dividing both sides by x^2,
we get,

=> x^2 -(10*x) + 5 + (100/x) +(100/x^2) = 0

=> x^2 + (10/x)^2 + 5 + (100/x) - (10*x) = 0

=> (x- 10/x)^2 + 20 + 5 - 10( x - 10/x) = 0

Now, let (x - 10/x) = K
=> K^2 + 25 -10K = 0
=> (K-5)^2 = 0
=> K=5

Now substituting the value of K, we get,
      x - 10/x = 5
=> x^2 - 5x - 10 = 0
=> x = [5 +√(25+40)]/2 and  x = [5-√(25+40)]/2

=> x = [5 +√65]/2 and  x = [5-√(65)]/2  ANS
Solution credit - Atyant Yadav
One can also solve it by breaking this eqaution into two quadratic but this approach is more feasible.

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