Question

If alpha and beta are zeroes of the polynomial {2x}2-5x+7 then find the quadratic Polynomial where zeroes are { 3 alpha + 4 beta } and {4 alpha + 3 beta }

Answer 1

let sum of roots -b/a= -7( alpha+beta)

product of roots c/a=12alpha*2+9alpha;beta+16alpha;beta+12beta*2

=12alpha*2+25alpha;beta+12beta*2

X*2-7(alpha+beta)+12(alpha*2+beta*2+24beta;alpha)+alpha;beta

let alpha be. =@

let beta be=$

for convince

given from above

(@+$)=5/2

-7(@+$)=-7(5/2)

@$=7/2

12(@+$)*2=12(25/4)

so the equation is

x*2-(-7(5/2))x+12(25/4)+7/2

x*2+19/2x+150/2+7/2

x*2+19/2x+157/2=0

2x*2+19x+157