Question

1 Find the zeroes of the following quadratic polynomials and verify the relationship between
the zeroes and the coefficients.
(vi) 3x2-x-4​

Answer 1

Given equation is x

2

−2x−8

x

2

−2x−8=x

2

−4x+2x−8

=x(x−4)+2(x−4)

=(x−4)(x+2)

The value of x

2

−2x−8 is zero when x−4=0 or x+2=0.

i.e, when x=4 or x=−2.

∴ The zeroes ofx

2

−2x−8 are 4 and −2.

sum of zeroes =4+(−2)=2

product of zeroes =−2×4=−8.

Relationship between the zeroes and the coefficients for the standard quadratic equation is ax

2

+bx+c=0

Sum of roots = −

a

b

and Product of roots =

a

c

In given equation

x

2

−2x−8=0

a=1,b=−2,c=−8

Sum of roots = −

1

−2

=2

and Product of roots =

1

−8

=−8

The relationship between the zeroes and the coefficients is verified.