Question

Find the zeroes of the following polynomials by factorisation method and verify the relations between the zeroes and the coefficients of the polynomials:
4x2– 3x – 1
3x2 + 4x – 4
5t2 + 12t+ 7​

Answer 1

Answer:

Answer

Let f(x)=4x

2

−3x−1

Splitting the middle term, we get

=4x

2

−4x+1x−1

=4x(x−1)+1(x−1)

=(x−1)(4x+1)

For f(x)=0, we have

4x

2

−3x−1=0

or (x−1)(4x+1)=0

Either x−1=0⇒x=1

or 4x+1=0

⇒4x=−1

⇒x=

4

−1

∴ The zeroes of f(x) are 1 and

4

−1

.

Verification:

α=1,β=

4

−1

a=4,b=−3 and c=−1

∴α+β=

a

−b

⇒1−

4

1

=

4

−(−3)

⇒

4

3

=

4

3

⇒LHS=RHS

Hence, verified

α.β=

a

c

⇒1×(

4

−1

)=

4

−1

⇒

4

−1

=

4

−1

⇒LHS=RHS

Hence, verified