# Help with the math exercise on roots of polynomial equations

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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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#2

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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.

**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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#4

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Yeah I have tried a number of times but can't figure out

**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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I dont know if it's the correct way to do. I just saw the answer behind and manipulated

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#9

(Original post by

X

**Shas72**)X

Now using the identity:

You know that so that gives two equations:

Any thoughts from here?

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#11

(Original post by

I did that first but couldn't get any solution.

**Shas72**)I did that first but couldn't get any solution.

Now this is a quadratic equation - can you see it?

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#13

(Original post by

So how do you get the final two quadratic equations

**Shas72**)So how do you get the final two quadratic equations

is a quadratic equation.

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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(Original post by

I'm not sure if you're noticing that this

is a quadratic equation.

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?

**Notnek**)I'm not sure if you're noticing that this

is a quadratic equation.

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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(Original post by

I couldn't understand how you got 4(alpha+beta)

**Shas72**)I couldn't understand how you got 4(alpha+beta)

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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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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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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

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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