Question

if alpha and beta are the zeros of of quadratic polynomial x square -6x +a find the value of a if 3 alpha +2beta=20

Answer 1

x²-6x+a
Roots are alpha and beta
Sum of roots=@+¥=-b/a=6
product of roots=c/a
alpha=@ and beta=¥
3@+2¥=20
@+2@+2¥=20
@+2(@+¥)=20
@+2(6)=20
@=8 Now beta=¥=-2
c/a
Here c is equal to a in the equation so a =¥@=8×(-2)=-16