Question

If p, q be non-zero real numbers and f(x) ≠ 0 for

∀ x ∈ [0,2] and

$\int_{0}^{1}{f(x).(x^{2} + px + q)dx}$ = $\int_{0}^{2}{f(x).(x^{2} + px + q)dx}$=0

Then equation x² + px + q = 0 has

• A. Two imaginary roots
• B. No root in (0, 2)
• C. One root in (0, 1) and other in (1, 2)
• D. One root in (–∞, 0) and other in (2, ∞)

Answer 1

Answer: (C)

One root in (0, 1) and other in (1, 2)

Answer 2

Since f(x) ≠ 0 then x² + px + q = 0 for some

x ∈ (0,1)

also $\int_{1}^{2}{f(x)(x^{2} + px + q)dx}$ = 0