Answer :

Solution :

Given polynomial, p(x) = x⁴ - 4x³ + 2

Using intermediate value theorem,

p(0) = 0 - 0 + 2 = 2 p(1) = 1 - 4 + 2 = -1

Since, p(0) > 0 .... (1)

p(1) < 0 .... (2)

From equation (1) and (2),

there exist a value 'x' in between 0 and 1

where, p(x) = 0

Hence, in the open interval (0, 1), the polynomial p(x) has one real root.