(Q17)Find the zeros of the following quadratic polynomials and verify the relationship between the zeros and the coefficients 3x2-x-4.

Answer:

Given polynomial is 3x2-x-4

we have,3x2-x-4=3x2+3x-x-4

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

=(x+)(3x-)

the value of 3x2-x-4 is 0 when the value of(x+)(3x-)is 0.

when x+=0 or 3x-=0

when x= - or x=
3
the zeros of 3x2-x-4 are - and
3

therefore sum of the zeros = - +
3
 =
3
= -
coefficient of x
coefficient of x2
 =
-(-)
3
 =
3

product of the zeros -×
3
=
-
3
= -
constant term
coefficient of x2
=
-
3