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KVPY2013MathematicsQuadratic Equation

The sum of non-real roots of the polynomial equation x³+3 x²+3 x+3=0 .

Options

  1. Aequals 0
  2. Blies between 0 and 1
  3. Clies between -1 and 0
  4. Dhas absolute value bigger than 1

Correct answer

C. lies between -1 and 0

Step-by-step solution

array l f(x)=x³+3 x²+3 x+3=0 f^ (x)=3 x²+6 x+3=3(x+1)² 0 f(x) is lncreasing function Now array l f(-3)=-6 0 array array real root lies between -3 and -2 + + =-3 ; -3 < < -2 array l + -3 < + + < + -2 + -3 < -3 < + -2 -1 < + < 0 array

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