Consider the cubic equation $x^3+c x^2+b x+c=0$ where $a, b, c$ are real numbers. Which of the following statements is correct?
Consider the cubic equation $x^3+c x^2+b x+c=0$ where $a, b, c$ are real numbers. Which of the following statements is correct?
- [KVPY 2011]
- A
If $a^2-2 b < 0$, then the equation has one real and two imaginary roots
- B
If $a^2-2 b \geq 0$, then the equation has all real roots.
- C
If $a^2-2 b > 0$, then the equation has all real and distinct roots.
- D
If $4 a^3-27 b^2 > 0$, then the equation has real and distinct roots.
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- [KVPY 2017]