Polynomial Properties

Algebra Level 3

Given two polynomials p ( x ) p(x) and q ( x ) q(x) such that they are cubic, which of the following statements doesn't hold true?

Note :-

∙ \bullet d ( P ( x ) ) d(P(x)) stands for degree of the polynomial p ( x ) p(x)

∙ \bullet This question is taken from TamilNadu-NTSE 2014 paper.

d ( p ( x ) − q ( x ) ) ≤ 3 d(p(x)-q(x))\leq3 d ( ( p ( x ) + q ( x ) ) = 3 d((p(x)+q(x))=3 d ( p ( x ) × q ( x ) ) = 6 d(p(x)\times q(x))=6 d ( p ( x ) 2 × q ( x ) 3 ) = 15 d(p(x)^2\times q(x)^3)=15

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Krishna Ar by Krishna Ar , 21, India

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1 solution

Sanjeet Raria
Nov 4, 2014

I'll give a counter example of the incorrect statement:

Consider P ( x ) = a x 3 a n d Q ( x ) = − a x 3 P(x)=ax^3 \space and \space Q(x)=-ax^3

Now P ( x ) + Q ( x ) = 0 P(x)+Q(x)=0 ⇒ d ( P ( x ) + Q ( x ) ) = 0 ≠ 3 \Rightarrow d(P(x)+Q(x))=0 \neq 3 Hence this statement isn't always correct. The rest are always true.

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Yeah. Right!

Krishna Ar - 6 years, 7 months ago

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its a very good question for Multiple Scenario section of SAT Math beta tag

U Z - 6 years, 7 months ago

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Yes..but SAT Beta doesnt having ratings yet.

Krishna Ar - 6 years, 7 months ago

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