(Q1)Find the zeros of the quadratic polynomials given below.Find the sum and product of the zeros and verify relationship to the coefficients of terms in the polynomial p(x) = x2 - x - 6.

Answer:

(i)Given polynomial p(x)=x2 - x -6

We have x2 - x -6=x2 - 3x+ x-6

= x(x- )+ (x-3)

=(x-3)(x+2)

So,the value of x2 - x-6 is zero when x- =0 or x+ =0

x= or x= -

So,the zeros of x2 - x -6 are and -

Sum of the zeros = - =

-
cofficient of x
cofficient of x2
 =
-(- )
1
 =

Product of the zeros = ×(- ) = -6

=
constant term
cofficient of x2
 =
-
1
 = -