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junior college 2 | H1 Maths
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How to show quadratic factor of p(x) is positive for all real values of x
Date Posted: 5 years ago
Views: 961
Look at the quadratic coefficient and the discriminant.
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I don't understand why b2-4ac smaller than 0 could become positive? The others factor you haven't prove is positive x2+3 determine whole px?
b²-4ac is the discriminant.
Key word is "always". Other factors can be positive/negative but not "always positive".
Key word is "always". Other factors can be positive/negative but not "always positive".
But b2-4ac get negative why can't use other factors to prove?
Firstly, do you know what the discriminant tells you?
And secondly, the question specifically asks for the quadratic factor. Hence we ignore the linear factors.
Sorry I am a noob please don't blame me.
What is discriminant
It is - 12 why still positive?
The discriminant tells you if your curve will cut the x axis or not. Positive means it will cut the x axis at 2 points. Zero means the x axis is a tangent to the curve, ie touch at one point. Negative means the curve and the x axis will never meet.
Then check the quadratic coefficient. Positive means curve is ∪ Shaped. Negative means ∩ shaped. Zero then it's no longer quadratic.
Then check the quadratic coefficient. Positive means curve is ∪ Shaped. Negative means ∩ shaped. Zero then it's no longer quadratic.
-12smaller than 0 determine what?
As I've said, it shows that the curve will never cut the x-axis. Meaning the whole graph will be floating above the x-axis, ie positive for all x∈R
Oh... Always positive is special meaning b2-4ac is negative no x whole graph float above x axis?
If the quadratic coefficient is positive then it floats above. If it's negative then float below.
Thank you so much l
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