JEE Advanced Maths: Basic Mathematics (Equations) questions with solutions

Q1. Solve the equation x⁴ - 2x³ - 2x² + 2x + 1 = 0.

1. x = 1, -1, 1 + sqrt(2), 1 - sqrt(2)
2. x = 1, -1, (3 + sqrt(5))/2, (3 - sqrt(5))/2
3. x = 1, 2, 3, -1
4. x = -1, -1, 2, 3

Answer: x = 1, -1, 1 + sqrt(2), 1 - sqrt(2)

x = 1 and x = -1 are roots by inspection, so x² - 1 is a factor. Dividing leaves the quadratic x² - 2x - 1 whose roots are 1 +/- sqrt(2).