Question

Find the value of a for which the equation 4x² − 2x + a = 0 has two different roots lying in the interval (− 1, 1).

Answer 1

First of all, the roots must be real and different. Therefore,

4 − 16 a > 0 ⇒ a < 1/4

The roots are

Hence, 

The second condition implies the first. Therefore,

1 − 4a < 9 or 4a > − 8 or a > − 2

Hence, − 2 < a < 1/4.