Question

find the root of function f(x) = (2^x-1).(x^2+2x-3) with x is a rational number​

Answer 1

Answer is given in the pic.

Answer 2

Answer:

x = -3 , 0 , 1

Step-by-step explanation:

Let f(x) = 0 , i.e.,

(2^x-1)(x^2+2x-3) = 0

Then,

2^x - 1 = 0  ---> (1)

2^x = 1

Taking log on both sides,

x = log 1 to the base 2

=>  x = 0

OR

x^2 + 2x - 3 = 0

x^2 + 3x - x - 3 = 0

x(x + 3) - 1(x + 3) = 0

(x + 3)(x - 1) = 0

x + 3 = 0   OR  x - 1 = 0

x = -3    OR    x = 1

Therefore,   x = -3 , 0 , 1

Hope it is useful...