Question

If f(x) : [1, 10] → Q be a continuous function. If f(x) takes rational value for all x and f(2) = 5 then the equation whose roots are f(3) and f(√10) is

(a) x2 –10x + 25 =0

(b) x2 –3x + 2 =0

(c) x2 –6x + 5 =0

(d) of these

Answer 1

Correct option(a)

Explanation:

Since f(x) is continuous in [1, 10]. f(x) will attain all values between f(1) and f(10). If f(1) ≠ f(10), then f(x) will attain innumerable irrational values between f(1) and f(10).

But given that f(x) attains rational values only, then we must have f(1) = f(10), infact f(x) = constant for x ∈ x8f[1, 10]. Since f(2) = 5, f(x) = f(2) = 5, ∀ x.

Hence the equation whose roots are f(3) and f (√10) is x2 – (5 + 5)x + 25 = 0.