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 2 years ago
The polynomial \(P(X) = a_0 + a_1X + a_2X^2 + ....+ a_nX^n\) where \(a_0,a_1,...,a_n\) are all real numbers and \(a_0>a_1>a_2>....>a_n>0\). Then which of the following MUST be true:
P(X) always has a real root
P(X) has a complex root z and z ≥1
P(X) has a complex root and z<1
P(X) does not have any complex root
 2 years ago
The polynomial \(P(X) = a_0 + a_1X + a_2X^2 + ....+ a_nX^n\) where \(a_0,a_1,...,a_n\) are all real numbers and \(a_0>a_1>a_2>....>a_n>0\). Then which of the following MUST be true: P(X) always has a real root P(X) has a complex root z and z ≥1 P(X) has a complex root and z<1 P(X) does not have any complex root

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ParthKohli
 2 years ago
Best ResponseYou've already chosen the best response.1Always assume a polynomial of this form. Use this for the experiments:\[\rm p(x) = x^2 + 2x + 3\]

ParthKohli
 2 years ago
Best ResponseYou've already chosen the best response.1Now see what all is true.

SheldonEinstein
 2 years ago
Best ResponseYou've already chosen the best response.1@ParthKohli Sorry, didn't get you, can you explain me more?

ParthKohli
 2 years ago
Best ResponseYou've already chosen the best response.1In these questions, I always take an example of a polynomial and see what all is true amongst the choices.

SheldonEinstein
 2 years ago
Best ResponseYou've already chosen the best response.1OK... i am getting it... let me check the choices now.

SheldonEinstein
 2 years ago
Best ResponseYou've already chosen the best response.1At least it will be complex root if I take your equation of the polynomial. P(X) = \(x^2+2x+3\) x = \(\LARGE\frac{2 \pm \sqrt{412}}{2} = \frac{2 \pm 2\sqrt{2}}{2} = 1 \pm \sqrt{2} i \)

SheldonEinstein
 2 years ago
Best ResponseYou've already chosen the best response.1So it will be ,,,, 2nd option : P(X) has a complex root z and z ≥1 Right?

ParthKohli
 2 years ago
Best ResponseYou've already chosen the best response.1Keep taking such equations and you'd get your answer... I think.

SheldonEinstein
 2 years ago
Best ResponseYou've already chosen the best response.1OK thanks for the shortcut friend...

ParthKohli
 2 years ago
Best ResponseYou've already chosen the best response.1\[\sqrt{(1)^2 + (\sqrt2)^2} = \sqrt{1 + 2} = \sqrt 3\]Yes, you're right

SheldonEinstein
 2 years ago
Best ResponseYou've already chosen the best response.1:) Yeah Yeah Yeah!!! Thanks!
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