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KVPY2011MathematicsQuadratic Equation

Consider the cubic equation x³+a x²+b x+c=0 , where a, b, c are real numbers. Which of the following statements is correct?

Options

  1. AIf a²-2 b < 0 , then the equation has one real and two imaginary roots
  2. BIf a²-2 b 0 , then the equation has all real roots
  3. CIf a²-2 b>0 , then the equation has all real and distinct roots
  4. DIf 4 a³-27 b²>0 , then the equation has real and distinct roots

Correct answer

A. If a²-2 b < 0 , then the equation has one real and two imaginary roots

Step-by-step solution

array l f(x)=x³+a x²+b x+c f^ (x)=3 x²+2 a x+b D=4 a²-4.3 b=4 (a²-3 b ) array If a² Hence f ( x )=0 has 1 real and two imaginary roots

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