C1 Solving inequalities exam question - help please

This question is C1 January 2006, Q10 part (d), for reference.

I got to k^(2)<12, and then k<=+/-2root3. I thought I should leave the answer as k<2root3, as k<-2root3 is inclusive in k<2root3.

The answer is -2root3<k<2root3, and I am not sure why. Could somebody explain please?

Thank you

Reply 1

B_9710

18

Thing about the graph of

y=x^2 -12

, to satisfy the inequality (replacing k with x) the curve must be below the x axis so that y<0.

You cannot just square root it when there is an inequality. By your logic -10 should satisfy the inequality, but does it in reality? No.

(edited 8 years ago)

Reply 2

Cryptokyo

14

It is k>-2root3 as the square of (-2root3) is 12. If we make it more negative then k^2 will be greater than 12.

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Reply 3

stochasym

12

I loved your explanation (http://www.wolframalpha.com/input/?i=plot+y%3Dx%5E2-12)
It is like finding the roots of X^2-12=0
Generally I try remembering that

x^{2}\leq a\Rightarrow-\sqrt{a}\leq x\leq\sqrt{a}

Original post by B_9710

Thing about the graph of

y=x^2 -12

, to satisfy the inequality (replacing k with x) the curve must be below the x axis so that y<0.

You cannot just square root it when there is an inequality. By your logic -10 should satisfy the inequality, but does it in reality? No.