GATE EE 2020 Question 1: Cubic Polynomial Roots & Properties | examprev.com

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Electrical Engineering > GATE 2020 > Algebra

ax³+bx²+cx+d is a polynomial on real x over real coefficients a, b, c, d wherein a≠0. Which of the following statements is true?

A

d can be chosen to ensure that x=0 is a root for any given set a, b, c.

B

No choice of coefficients can make all roots identical.

C

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

D

c alone cannot ensure that all roots are real.

Correct : a

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