For the equation $|{x^2}| + |x| - 6 = 0$, the roots are

  • A

    One and only one real number

  • B

    Real with sum one

  • C

    Real with sum zero

  • D

    Real with product zero

Similar Questions

Let $p(x)=a_0+a_1 x+\ldots+a_n x^n$ be a non-zero polynomial with integer coefficients. If $p(\sqrt{2}+\sqrt{3}+\sqrt{6})=0$, then the smallest possible value of $n$ is

  • [KVPY 2009]

Exact set of values of $a$ for which ${x^3}(x + 1) = 2(x + a)(x + 2a)$ is having four real solutions is

If $\alpha, \beta$ are the roots of the equation, $x^2-x-1=0$ and $S_n=2023 \alpha^n+2024 \beta^n$, then

  • [JEE MAIN 2024]

If $a < 0$ then the inequality $a{x^2} - 2x + 4 > 0$ has the solution represented by

If $S$ is a set of $P(x)$ is polynomial of degree $ \le 2$ such that $P(0) = 0,$$P(1) = 1$,$P'(x) > 0{\rm{ }}\forall x \in (0,\,1)$, then

  • [IIT 2005]