Question

If f(x) satisfies the equation |(f(x + 1), f(x + 8), f(x + 1)), (1, 2, -5), (2, 3, λ)| = 0 for all real x and if f is periodic with period 7, then find the value of |λ|.

Answer 1

On solving, we get

(2λ + 15) f(x + 1) - (λ+ 10) f(x + 8) - f(x + 1) = 0

⇒ (2λ + 14) f(x + 1) = (λ+ 10) f(x + 8)

Since, f is periodic with period 7, therefore

f(x + 1) = f(x + 8)

⇒ 2λ + 14 = λ + 10

⇒ |λ| = 4