If both the roots of the equation x 2 - m x + 1 = 0 are less than unity, then

Step-by-step solution

f x = x 2 - m x + 1 and α ≤ β are the roots of f x = 0 . Now, α < β < 1 implies that f 1 and the coefficients of x 2 have the same sign. This gives f 1 > 0 ⇒ 1 - m + 1 > 0 ⇒ m < 2 Also, the discriminant is m 2 - 4 ≥ 0 . So m ≤ - 2 or m ≥ + 2 . Taking intersection, we get, m ≤ - 2 . Also, note that if m = - 2 , the roots are - 1 , - 1 .