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

Solution:

Let α and β be the zeros of the polynomial 2x^{2} -5x -3

Then α + β = 5/2

And αβ = -3/2.

Let 2α and 2β be the zeros x^{2} + 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