Multiple choice

The set of values of k for which roots of the equation ${ x }^{ 2 }\quad -\quad 3x\quad +\quad k\quad =\quad 0$ lie in the interval (0, 2), is :

  1. $\left( 2,\quad \infty \right) $
  2. $\left( 0,\quad \infty \right)$
  3. $\left( -\infty ,\quad 9/4 \right) $
  4. $\left( 2,\quad 9/4 \right) $
Reveal answer Fill a bubble to check yourself
B Correct answer
AI explanation

For the roots of x^2 - 3x + k = 0 to lie in (0, 2), the sum of the roots is 3, which cannot happen if both roots are strictly between 0 and 2. If one root is in (0, 2) and the other is outside, applying this interval constraint correctly requires k > 0. Therefore, the set of values for k is (0, infinity).

Keep practicing — related questions