V is more powerful than I

Algebra Level 1

Find the interval of $v$ which satisfies the inequality $(v+2)^2(v-4)(v-6)<0.$

(-2,4)

[4,6]

(-2,6)

(4,6)

3 solutions

Hjalmar Orellana Soto
Nov 24, 2015

As $(u+2)^{2}$ is always positive (for real $u$ ) we are looking for an interval where $(v-4)(v-6)<0$ . As $(v-4)(v-6)$ represents a concave parabola which intersects $x$ axis at $x=4$ and (x=6), so the interval we are looking for is $(4,6)$

I think that we have a notation problem. (4,6) is mainly used as notation for coordinate not as an interval. ]4,6[ would have been the best notation for open interval.

Paraison Gérard Jimmy - 5 years, 5 months ago

I second you. It should be ]4,6[

Nader Selim - 5 years, 5 months ago

I put [4,6]. What's the difference between this and (4,6)?

Andy Wright - 5 years, 5 months ago

i also put [4,6] because there was not ]4,6[ instead (4,6) seems like the coordinate of a point

Mario Kerciku - 5 years, 5 months ago

I agree (4,6) implies a coordinate.

Anne Turton - 5 years, 5 months ago

[4,6] means the interval is inclusive of 4 and 6, so 4 ≤ x ≤ 6.

(4,6) means the interval does not include 4 and 6, so 4 < x < 6.

As David Ortiz said below, "substituting 4 yields 0<0, which is not true..." and substituting 6 also yields 0<0, so 4 and 6 are not within the solution. Therefore 4 < x < 6, so the answer is (4,6).

James Nicolora - 5 years, 5 months ago

Fair enough. It seems though that this is less of a maths problem than one of knowing obscure notation

Andy Wright - 5 years, 5 months ago

This notation isn't correct. Righting 4<x<6 <=> x € ]4 ; 6[

Frédéric Deleria - 5 years, 4 months ago

@Frédéric Deleria – That could be another way to write it. I haven't seen that notation before to be honest. Math is universal but does notation vary from place to place?

James Nicolora - 5 years, 4 months ago

[4,6] includes four and six where (4,6) is only the numbers between them

Morgan McKinnon - 4 years, 11 months ago

David Ortiz
Dec 27, 2015

Utilizing the fact that the question is multiple choice, you could start by trying to plug in 0. The result is positive, so zero is not a solution which brings your choices to [4,6] or (4,6). Substituting 4 yields 0<0, which is not true, so 4 is not a solution and thus the answer must be (4,6).

Victor S
Jun 21, 2016

4 and 6 can't be in the intervalo because the product is zero.

V is more powerful than I

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