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If the zeroes of the polynomial x2 +px +q are double in value to the zeroes of the polynomial 2x2 -5x -3, then find the values of p and q.

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Solution:

Let α and β be the zeros of the polynomial 2x2 -5x -3 

Then α + β = 5/2 

And αβ = -3/2. 

Let 2α and 2β be the zeros x2 + px +q 

Then 2α + 2β = -p 

 2(α + β) = -p 

 2 x 5/2 =-p 

So p = -5 

And 2α x 2β = q 

 4 αβ = q 

 So q = 4 x-3/2 

        = -6

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