1.

Find the zeros of polynomial 6x² - 3 - x​

Answer»

Answer:

Step-by-step explanation:

We have,

f(x)=6x

2

−3

→ f(X)=(

6

​

x)

2

−(

3

​

)

2

→ f(x)=(

6

​

x−

3

​

)(

6

​

x+

3

​

)

The zeros of f(x) are GIVEN by f(x) =0

ie., (

6

​

x−

3

​

)(

6

​

x+

3

​

)=0

⇒

6

​

x−

3

​

=0 or,

6

​

x+

3

​

=0

⇒ x=

6

​

3

​

​

or, x=

6

​

−

3

​

​

⇒ x=

2

​

1

​

or x=−

2

​

1

​

Hence, the zeros of f(x)=6x

2

−3 are: α=

2

​

1

​

= and β=−

2

​

1

​

Now,

SUM of the zeros = α+β=

2

​

1

​

+(−

2

​

1

​

)=0

Sum of the zeros = -

COEFFICIENT of x

2

Coefficient of x

​

∴ -

Coefficient of x

2

Coefficient of x

​

=−

6

0

​

=0

Also,

Product of the zeros = αβ =

2

​

1

​

×

2

​

−1

​

=

2

−1

​

and,

∴ Product of the zeros=

Coefficient of x

2

Constant term

​

=

6

−3

​

=

2

−1

​

Hence verified.I HOPE it helps you ✅✅


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