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# Solving Quadratic Inequalities: Graphical Approach

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Re: Solving Quadratic Inequalities: Graphical Approach [#permalink]
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pearljiandani wrote:
Hi Bunuel

I read this post of yours and it was extremely helpful. However I'm a little confused, it'll be great if you can help me out here. So in this post, it says that if the sign is "<", it means that x lies between the 2 roots and if the sign is ">", then x lies on the left of the smaller root and on the right of the bigger root. Now I was solving this other question -

If x^2 + 2x -15 = -m, where x is an integer from -10 and 10, inclusive, what is the probability that m is greater than zero?

A. 2/7
B. 1/3
C. 7/20
D. 2/5
E. 3/7

Re-arrange the given equation: −x^2−2x+15=m

Given that xx is an integer from -10 and 10, inclusive (21 values) we need to find the probability that −x^2−2x+15 is greater than zero, so the probability that −x^2−2x+15>0

Factorize: (x+5)(3−x)>0. This equation holds true for −5<x<3

Since x is an integer then it can take the following 7 values: -4, -3, -2, -1, 0, 1, and 2.

Here, if (x+5)(3−x)>0, then shouldn't x be smaller than -5 and greater than 3? I know that doesn't satisfy the equation given in the question but I was wondering how this was possible if the sign ">" meant that the solution lies on the left of the smaller root and on the right of the bigger root.

Rewrite (x+5)(3−x)>0 as (x+5)(x−3)<0 (so that you have (x +/- something )(x +/- something) ) --> -5 < x < 3.

Or if you expand: (x+5)(3−x)>0 you get -x^2 - 2 x + 15 > 0. Rewrite as x^2 + 2x - 15 < 0. --> roots are -5 and 3 and < indicates between the roots: -5 < x < 3.

Hope it's clear.
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Re: Solving Quadratic Inequalities: Graphical Approach [#permalink]
Bunuel wrote:
pearljiandani wrote:
Hi Bunuel

I read this post of yours and it was extremely helpful. However I'm a little confused, it'll be great if you can help me out here. So in this post, it says that if the sign is "<", it means that x lies between the 2 roots and if the sign is ">", then x lies on the left of the smaller root and on the right of the bigger root. Now I was solving this other question -

If x^2 + 2x -15 = -m, where x is an integer from -10 and 10, inclusive, what is the probability that m is greater than zero?

A. 2/7
B. 1/3
C. 7/20
D. 2/5
E. 3/7

Re-arrange the given equation: −x^2−2x+15=m

Given that xx is an integer from -10 and 10, inclusive (21 values) we need to find the probability that −x^2−2x+15 is greater than zero, so the probability that −x^2−2x+15>0

Factorize: (x+5)(3−x)>0. This equation holds true for −5<x<3

Since x is an integer then it can take the following 7 values: -4, -3, -2, -1, 0, 1, and 2.

Here, if (x+5)(3−x)>0, then shouldn't x be smaller than -5 and greater than 3? I know that doesn't satisfy the equation given in the question but I was wondering how this was possible if the sign ">" meant that the solution lies on the left of the smaller root and on the right of the bigger root.

Rewrite (x+5)(3−x)>0 as (x+5)(x−3)<0 (so that you have (x +/- something )(x +/- something) ) --> -5 < x < 3.

Or if you expand: (x+5)(3−x)>0 you get -x^2 - 2 x + 15 > 0. Rewrite as x^2 + 2x - 15 < 0. --> roots are -5 and 3 and < indicates between the roots: -5 < x < 3.

Hope it's clear.

Yes it's clear now, thank you! Bunuel
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Re: Solving Quadratic Inequalities: Graphical Approach [#permalink]
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Re: Solving Quadratic Inequalities: Graphical Approach [#permalink]
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