#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.