Question

If alpha and beta are zeros of the quadratic polynomial x2 -6x +a find a if 3 alpha +2 beta =20

Answer 1

given equation x2-6x+a
from equation
alpha+beta =6
so, alpha = 6- beta.............(i)
alpha*beta=a
given condition 3alpha+2beta=20......(ii)
putting(i) in (ii),we get
3(6-beta) + 2beta= 20
18-3beta+2beta=20
18-beta=20
-beta=2
beta= -2

putting beta=-2 in alpha*beta=a, we get
a= 8*-2
a= -16