Multiple choice

If $k\in R$, One root of the equation $(2k1){x}^{2}-kx+k-2=0$ is less than $1$ and the other greater than $1$ if

  1. $-\frac{1}{2}<k<\frac{1}{2}$
  2. $k>\frac{1}{2}$
  3. $k<-\frac{1}{2}$
  4. $0<k<1$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

For the equation (2k+1)x^2 - kx + (k-2) = 0, substituting x = 1 gives f(1) = 2k - 1. The condition for one root less than 1 and the other greater than 1 is a*f(1) < 0, so (2k+1)(2k-1) < 0, which yields -1/2 < k < 1/2.

Keep practicing — related questions