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secondary 3 | A Maths
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Ivan
Ivan

secondary 3 chevron_right A Maths chevron_right Singapore

Pls help with this question. Thanks.

Date Posted: 4 years ago
Views: 233

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Arnold K H Tan
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2163 answers (A Helpful Person)
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Ivan
Ivan
4 years ago
Why is x <= -8? And not >= -8?
Arnold K H Tan
Arnold K H Tan
4 years ago
Based on the graph sketch on the right as working: x² + 10x + 16 >= 0 means you want the values of x for which the graph is above the x-axis (shaded light blue).

You can easily verify the solution is correct by substitution. For example, when x = -10, (-10)² + 10(-2) + 16 = 96, which is greater than 0.
Ivan
Ivan
4 years ago
I see. Thank you!
Eric Nicholas K
Eric Nicholas K
4 years ago
Quadratic inequalities do not function the same way as linear inequalities do!

When we learn to solve linear inequalities such x + 8 > 0, we can simply say that x > -8. This is true because when we plot a graph of y = x + 8 on an x-y plane, the graph goes above the x-axis after x = -8 and never ever goes back below the x-axis.

Quadratic inequalities are trickier.

(x + 8) (x + 2) > 0

It appears as though x + 8 > 0 or x + 2 > 0. However, unlike the case of the linear inequality, the shape of the graph of this function is different.

It starts out high above the x-axis. It then crosses over to below the x-axis for a short period of time before returning above the x-axis.

As such, it is not immediately true that the solution fitting the inequalities satisfy x + 8 > 0 or x + 2 > 0.

In fact, x + 8 < 0 or x + 2 > 0.
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Lee Hui Xian
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2 answers (Tutor Details)
Hope it helps