The number of real roots of the equation, e 4 x + e 3 x - 4 e 2 x + e x + 1 = 0 is:

Question

Aicharya · Accepted Answer

Let e x = t &#8712; 0 , &#8734; Given equation t 4 + t 3 - 4 t 2 + t + 1 = 0 t 2 + t - 4 + 1 t + 1 t 2 = 0 t 2 + 1 t 2 + t + 1 t - 4 = 0 Let t + 1 t = &#945; &#945; 2 - 2 + &#945; - 4 = 0 &#945; 2 + &#945; - 6 = 0 &#945; 2 + &#945; - 6 = 0 &#945; = - 3 , 2 &#8658; &#945; = 2 &#8658; e x + e - x = 2 x = 0 is the only solution.

The number of real roots of the equation, e 4 x + e 3 x - 4 e 2 x + e x + 1 = 0 is:

Solution