Question

If all real values of x obtained from the equation

4^x – (a – 3) 2^x + a – 4 = 0 are non positive then

• A. aĪ(4, 5]
• B. aĪ(0, 4)
• C. aĪ(4, )
• D. None

Answer 1

Answer: (A)

aĪ(4, 5]

Answer 2

(2^x)² – (a – 3) 2^x + a – 4 = 0 Let 2^x = y

y² – (a – 3)y + a – 4 = 0

y² – (a – 4) y – y + a – 4 = 0

Ž y(y – a + 4) – 1(y – a + 4) = 0

Ž (y – a + 4) (y – 1) = 0 Ž y = a – 4, y = 1

hence 2^x = 1 & 2^x = a – 4 Q x £ 0

hence 0 < a – 4 £ 1 Ž 4 < a £ 5