Question

The number of distinct real roots of x⁴ - 4x³ + 12x² + x - 1 = 0 is ......

Answer 1

Let f(x) = x⁴ - 4x³ + 12x² + x - 1 = 0

f' (x) = 4x³ - 12x² + 24 + 1 = 4(x³ - 3x² + 6x) + 1

f'' (x) = 12x² - 24x + 24 = 12(x² - 2x + 2)

Therefore, f''(x) has 0 real roots.

Hence, f (x) has maximum 2 distinct real roots as f (0) = −1.