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SheldonEinstein
Group Title
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
 one year ago
 one year ago
SheldonEinstein Group Title
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
 one year ago
 one year ago

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

ParthKohli Group TitleBest ResponseYou've already chosen the best response.1
Now see what all is true.
 one year ago

SheldonEinstein Group TitleBest ResponseYou've already chosen the best response.1
@ParthKohli Sorry, didn't get you, can you explain me more?
 one year ago

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

ParthKohli Group TitleBest ResponseYou've already chosen the best response.1
Hindi mein bolun?
 one year ago

SheldonEinstein Group TitleBest ResponseYou've already chosen the best response.1
OK... i am getting it... let me check the choices now.
 one year ago

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

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

ParthKohli Group TitleBest ResponseYou've already chosen the best response.1
Keep taking such equations and you'd get your answer... I think.
 one year ago

SheldonEinstein Group TitleBest ResponseYou've already chosen the best response.1
OK thanks for the shortcut friend...
 one year ago

ParthKohli Group TitleBest ResponseYou've already chosen the best response.1
z is the modulus?
 one year ago

SheldonEinstein Group TitleBest ResponseYou've already chosen the best response.1
Yeah
 one year ago

SheldonEinstein Group TitleBest ResponseYou've already chosen the best response.1
It is modulus.
 one year ago

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

SheldonEinstein Group TitleBest ResponseYou've already chosen the best response.1
:) Yeah Yeah Yeah!!! Thanks!
 one year ago

ParthKohli Group TitleBest ResponseYou've already chosen the best response.1
You're welcome ;)
 one year ago
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