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# Vieta's formula application

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\(f(x) = x^2-kx+18\). One root is twice the other. Find the roots.

I got 3 and 6 from this since Vieta's formula says that the product of the roots must be 18 and 3*2 = 6. Did I do it correctly?

Nov 15, 2020

#1
+9198
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Let  a  and  b  be the roots. Then we can make these two equations:

ab  =  18     and     a  =  2b

Substituting  2b  in for  a  into the first equation, we get:

(2b)b  =  18

2b2  =  18

b2   =   9

b   =   ± 3

Which means.....

a   =   2 * (± 3)

a   =   ± 6

So  3  and  6  is one possible solution,  and the other possible solution is  -3  and  -6

Nov 15, 2020

#1
+9198
+1

Let  a  and  b  be the roots. Then we can make these two equations:

ab  =  18     and     a  =  2b

Substituting  2b  in for  a  into the first equation, we get:

(2b)b  =  18

2b2  =  18

b2   =   9

b   =   ± 3

Which means.....

a   =   2 * (± 3)

a   =   ± 6

So  3  and  6  is one possible solution,  and the other possible solution is  -3  and  -6

hectictar Nov 15, 2020