Question

show that 12 and -32 are the zeroes of the polynomial 4x^2+4x-3 and verify the relationship between zeroes the coefficients of polynomial .​

Answer 1

Step-by-step explanation:

Let f(x)=4x

2

−4x−3

By splitting the middle term, we get f(x)=4x

2

−6x+2x−3

=2x(2x−3)+1(2x−3)

=(2x+1)(2x−3)

On putting f(x)=0, we get (2x+1)(2x−3)=0

⇒2x+1=0 or 2x−3=0

⇒x=

2

−1

Or x=

2

3

Thus, the zeroes of the given polynomial 4x

2

−4x−3 are

2

−1

and

2

3

Verification:

Sum of zeroes =α+β=

2

−1

+

2

3

=

2

−1+3

=1

=−

Coefficient of x

2

Coefficient of x

=−

4

(−4)

=1

Product of zeroes =αβ=

2

−1

×

2

3

=

4

−3

=

Coefficient of x

2

Constant term

=

4

−3

So, the relationship between the zeroes and the coefficients is verified.