The number of values of k for which the equation x2 - 3x + k = 0 has two distinct roots lying in the interval (0, 1) are

Question

The number of values of k for which the equation x2 - 3x + k = 0 has two distinct roots lying in the interval (0, 1) are (A) Three (B) Two (C) Infinitely many (D) No values of k satisfies the requirement

Tardigrade Admin · Accepted Answer

As -(b/2a)=(3/2)∉(0, 1), so both roots can not lie between 0 and 1. So no values of k possible.

Q. The number of values of $k$ for which the equation $x^{2} - 3 x + k = 0$ has two distinct roots lying in the interval $(0, 1)$ are

Three

Two

Infinitely many

No values of k satisfies the requirement

As $- \frac{b}{2 a} = \frac{3}{2} \in / (0, 1),$ so both roots can not lie between 0 and 1. So no values of k possible.

Q. The number of values of k for which the equation x2−3x+k=0 has two distinct roots lying in the interval (0,1) are

Three

Two

Infinitely many

No values of k satisfies the requirement

As −2ab​=23​∈/(0,1), so both roots can not lie between 0 and 1. So no values of k possible.

Q. The number of values of $k$ for which the equation $x^{2} - 3 x + k = 0$ has two distinct roots lying in the interval $(0, 1)$ are

As $- \frac{b}{2 a} = \frac{3}{2} \in / (0, 1),$ so both roots can not lie between 0 and 1. So no values of k possible.