Prelim 2016 Maths Help Thread (1 Viewer)

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Green Yoda

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For which values of k does (2k-3)x^2+(k+1)x-1=0 has two roots.
I know how to do these questions but the answer says k>1 or k<-11
Is this wrong? as I get the delta as k^2+10k-10
 

InteGrand

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For which values of k does (2k-3)x^2+(k+1)x-1=0 has two roots.
I know how to do these questions but the answer says k>1 or k<-11
Is this wrong? as I get the delta as k^2+10k-10
 

Suu

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HMm, just wondering, how would you find the derivative of a circle?
 

leehuan

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HMm, just wondering, how would you find the derivative of a circle?
The idea is that a derivative isn't strictly defined in terms of one variable if we're talking about implicit functions, which is what a circle is.

A circle is not actually a function because it fails the vertical line test. That's why you have to do what InteGrand did and consider two relevant semi-circles
 

Suu

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The idea is that a derivative isn't strictly defined in terms of one variable if we're talking about implicit functions, which is what a circle is.

A circle is not actually a function because it fails the vertical line test. That's why you have to do what InteGrand did and consider two relevant semi-circles
Ahh, I see now ^^
I spent a bit too much time on the bus two days ago thinking about derivation ^^
 

Green Yoda

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for what values of m is the following real
x^2+2mx+2(m+12)=0
I got m<=-4 or m>=6
but the answer is m<=-4 or m>6, why so?
 

InteGrand

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The roots will be real if and only if the discriminant is non-negative (doesn't need to be strictly positive; when the discriminant is 0, the roots are real, but they're identical, i.e. double root).
 

Nailgun

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But isnt it Δ>=0 for real values cuz Δ=0 is still an real value?
This is correct

delta is only imaginary when it is less than 0

this is because in quad formula delta is square rooted

can't square root a negative number and get real answers

however you can square root 0 and postiives
 
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