# Help with the math exercise on roots of polynomial equations

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#1
A quadratic equation has roots alpha and beta. Given that 1/ alpha +1/beta=1/2 and alpha^2+beta^2=12, find two possible quadratic equations that satisfy these values.
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1 year ago
#2
(Original post by Shas72)
A quadratic equation has roots alpha and beta. Given that 1/ alpha +1/beta=1/2 and alpha^2+beta^2=12, find two possible quadratic equations that satisfy these values.
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#3
Yeah I have tried a number of times but can't figure out
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1 year ago
#4
(Original post by Shas72)
Yeah I have tried a number of times but can't figure out First rearrange that so it's in a nicer form. If you've already done this, post your working.
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#5
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#6
I dont know if it's the correct way to do. I just saw the answer behind and manipulated
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#7
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#8
It's the 8th sum
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1 year ago
#9
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#10
I did that first but couldn't get any solution.
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1 year ago
#11
(Original post by Shas72)
I did that first but couldn't get any solution.
Combining the equations gives Now this is a quadratic equation - can you see it?
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#12
So how do you get the final two quadratic equations
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1 year ago
#13
(Original post by Shas72)
So how do you get the final two quadratic equations
I'm not sure if you're noticing that this If you let then you have If you solve this then you have two values for which in turn gives you two values for . This is enough to know what the final quadratic equations are - there's no need to find and . Make sense?
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#14
I will surely try to do your method. Thanks a tonne for helping.
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#15
I couldn't understand how you got 4(alpha+beta)
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#16
(Original post by Shas72)
I couldn't understand how you got 4(alpha+beta)
Oh yeah I got it you substituted it in the second equation.
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#17
How do you get the equations x^2-2x+4 and x^2-6x+12. Do you divide the 4 and 12 from 2
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#18
I got it fully. Thanks thanks thanks a lottttttt. Thanks a tonne for helping me. You are just too good!!!!!! Thanks again
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#19
Can you also pls help me with this one. The quadratic equation 3x^2+2x-4 has roots alpha and beta. Find the values of s1,s2 and s-1.
I finished solving s1 and s1 got the answers s1=-b/a=-2/3 and s2= alpha^2+beta^2= 28/9. I don't know how to find s-1. Pls help
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#20
I got this one. Tried again got this one.
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