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Q#1 Calculus GATE EE 2020 MSQ +1 mark -0 marks

 is a polynomial on real  over real coefficients  wherein. Which of the following statements is true?

No choice of coefficients can make all roots identical.

a, b, c, d can be chosen to ensure that all roots are complex.

d can be chosen to ensure that  is a root for any given set .

c alone cannot ensure that all roots are real.

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