Question

if alpha and bita are the zeroes of the quad poly. p{x}=2x^2-5x+7,find the polynomial whose zeroes are {2alpha +3bita} and {3alpha+2bita}

Answer 1

given - alpha + beta =(-5/2)=5/2 and alphabeta =7/2.
donate s and p for sum and product.
s=(2alpha + 3beta)+(3alpha+2beta)=5(alpha + beta)= 5×5/2=25/2
p=(2alpha+3beta)(3alpha+2beta)=6(alpha square + beta square)+13alpha beta =6alpha square + 6 beta square + 12 alpha beta + alpha beta.
=6(alpha+ beta) square + alpha beta
=6×(5/2)square + 7/2 = 75/2+7/2= 41

answer= x square -25/2x+41.