GATE 2020 EE Q.1: official answer

GATE 2020 · EEQ.1 · 1 mark · MCQ

$a x^{3} + b x^{2} + c x + d$ is a polynomial on real $x$ over real coefficients $a, b, c, d$ wherein $a \neq = 0$ . 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.

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GATE 2020 EE question 1

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Official answer

Official answer: A or DSource: Official answer key, GATE 2020 EE (IIT Delhi)

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