Question

find zeroes of polynomial
$4 \sqrt{3} x^{2} - 3 \sqrt{3} x - 2 \sqrt{3}$
and verify the relation of sum of zeroes and product of zeroes
​

Answer 1

Answer:

et p(x)=x  

2

−3

Zero of the polynomial is the value of x where p(x)=0

Put p(x)=0⇒x  

2

−3=0

⇒x  

2

−(  

3

​  

)  

2

=0

So,x=  

3

​  

,−  

3

​  

 

∴α=  

3

​  

 and β=−  

3

​  

 are zeroes of the polynomial.

We can write p(x)=x  

2

−3=x  

2

+0−3 is of the form ax  

2

+bx+c where a=1,b=0,c=−3

L.H.S=Sum of the zeroes=α+β=  

3

​  

−  

3

​  

=0

and R.H.S=Sum of the zeroes=  

a

−b

​  

=  

1

−0

​  

=0

L.H.S=Product of the zeroes=αβ=  

3

​  

×−  

3

​  

=−3

and R.H.S=product of the zeroes=  

a

c

​  

=  

1

−3

​  

=−3

Since L.H.S=R.H.S

Hence relationship between zeroes and coefficient is verified.

Step-by-step explanation: