Let   be non-zero real numbers such that Then, the quadratic equation  has a) No root in (0, 2) b) At least one root in (1, 2) c) A double root in (0, 2) d) Two imaginary roots

Question ID - 100022 :- Let   be non-zero real numbers such that Then, the quadratic equation  has a) No root in (0, 2) b) At least one root in (1, 2) c) A double root in (0, 2) d) Two imaginary roots

3537

(b)

Consider

Obviously,  is continuous and differentiable on [1, 2] and (1, 2) respectively.

Also,         (given)

By Rolle’s  theorem there exist at least one point  such that

Now,

is root of

Where

Hence, at least one root

Next Question :

There is a number series following a pattern.  One place is left blank.  Find the correct answer from the options.

 C, Z, F, X, I, V, L, T, O, ?, ? (a) O, P (b) P, Q (c) R, R (d) S, R