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Algebra Level 4

Let the number of real negative roots the polynomial f ( x ) f(x) have be Y \large{Y} . Find Y + 100 \large{Y}+100

f ( x ) f(x) = = 2 x 4 − x 3 + 4 x 2 − 5 x + 200 2x^{4}-x^{3}+4x^{2}-5x+200

Please don't use W O L F R A M WOLFRAM A L P H A ALPHA .


The answer is 100.

Harsh Shrivastava by Harsh Shrivastava , 20, India

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3 solutions

Harsh Shrivastava
Nov 21, 2014

Hint : Descartes' Rule of Signs

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Nayanmoni Baishya
Nov 21, 2014

The odd degree terms already have a negative sign.

2 Helpful 0 Interesting 0 Brilliant 0 Confused
Joe Mansley
Jul 12, 2015

Using Descartes' rule of signs, if we switch the signs of the odd degree terms, then there are no sign changes. So there are no negative roots and Y=0;

0+100=100

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