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Consider the cubic equation x^3 + ax^2 +...

Consider the cubic equation `x^3 + ax^2 + bx + c = 0`, where `a, b, c` are real numbers, which of the following statements is correct?

A

If `a^2 2b lt0,`then the equation has one real and two imaginary roots

B

If `a^2 -2b=0,` then the equation has all real and equal roots

C

If ` a^2 -2b gt 0` , then the equation has all real and distinct roots

D

If `4a^3 - 27b^2 gt0`, then the equation has real and distinct roots

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The correct Answer is:
A
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