Question

The roots of the equation (b + c)x² – (a + b + c)x + a = 0 (a, b, c ∈ Q, b + c ≠ a) are ______.

पर्याय

• irrational and different

• rational and different

• imaginary and different

• real and equal

Answer 1

The roots of the equation (b + c)x² – (a + b + c)x + a = 0 (a, b, c ∈ Q, b + c ≠ a) are rational and different.

Explanation:

∵ a, b, c ∈ Q, b + c ≠ a

⇒ a + b + c ∈ Q, b + c ∈ Q

∵ D = (a + b + c)² – 4(b + c)a

= (a – b – c)² 

Clearly roots are rational and different