(Q8)Find the quadratic polynomial whose zeros are 2 and
-1
3
.

Answer

Let the quadratic polynomial be ax2+bx+c,a≠0 and its zeros be α and β

Here α=2, β=
-1
3
Sum of the zeros =(α+β)=+(
-
) =

Product of the zeros =(αβ)=(
-
) =
-

therefore the quadratic polynomial ax2+bx+c is

k[x2-(α+β)x+αβ],where k is a constant and k≠0

k[x2 -
x -
]

We can take different values of k

When k = 3 the quadratic polynomial wil be 3x2-x - 2.