If $x$ is real, the function $\frac{{(x - a)(x - b)}}{{(x - c)}}$ will assume all real values, provided

  • [IIT 1984]
  • A

    $a > b > c$

  • B

    $a < b < c$

  • C

    $a > c < b$

  • D

    $a < c < b$

Similar Questions

The number of distinct real roots of the equation $x^{5}\left(x^{3}-x^{2}-x+1\right)+x\left(3 x^{3}-4 x^{2}-2 x+4\right)-1=0$ is

  • [JEE MAIN 2022]

Let $\mathrm{S}$ be the set of positive integral values of $a$ for which $\frac{\mathrm{ax}^2+2(\mathrm{a}+1) \mathrm{x}+9 \mathrm{a}+4}{\mathrm{x}^2-8 \mathrm{x}+32}<0, \forall \mathrm{x} \in \mathbb{R}$. Then, the number of elements in $\mathrm{S}$ is :

  • [JEE MAIN 2024]

If the inequality $kx^2 -2x + k \geq  0$ holds good for atleast one real $'x'$ , then the complete set of values of $'k'$ is

Let $a, b, c, d$ be real numbers between $-5$ and $5$ such that  $|a|=\sqrt{4-\sqrt{5-a}},|b|=\sqrt{4+\sqrt{5-b}},|c|=\sqrt{4-\sqrt{5+c}}$ $|d|=\sqrt{4+\sqrt{5+d}}$ Then, the product $a b c d$ is

  • [KVPY 2017]

The integer $'k'$, for which the inequality $x^{2}-2(3 k-1) x+8 k^{2}-7>0$ is valid for every $x$ in $R ,$ is

  • [JEE MAIN 2021]