Question

if alpha and beta are the zeroes of the polynomial 2x^2-5x+7 find a polynomial whose zeroes are 2alpha+3beta and 3alpha+2beta

Answer 1

2x²-5x-7
2x²+2x-7x-7
2x(x+1)-7(x+1)
(2x-7)(x+1)
Therefore alpha=7/2 and beta=-1
2(7/2)+3(-1)=alpha for the new polynomial ,=7-3=4
3(7/2)+2(-1)=beta for nsw polynomial ,=21/2-2=17/2
Hence the polynomial Will be x²-(4+17/2)x+4*17/2=x²-(25/2)x+34
2x²-25+68=0