Question

Find all the zeros and verify the relationship between coffcient (a) 2x^2-9. (b) x^3-2x^2

Answer 1

Answer:

Let f(x)=r  

2

s  

2

x  

2

+6rstx+9t  

2

 

Now, if we recall the identity (a+b)  

2

=a  

2

+b  

2

+2ab

Using this identity, we can write r  

2

S  

2

x  

2

+6rstx+9t  

2

=(rsx+3t)  

2

 

On putting f(x)=0, we get (rsx+3t)  

2

=0

⇒x=  

rs

−3t

​

,  

rs

−3t

​

 

Thus, the zeroes of the given polynomial r  

2

s  

2

x  

2

+6rstx+  

9t  

2

 are  

rs

−3t

​

 and  

rs

−3t

​

 

Verification:

Sum of zeroes =α+β=  

rs

−3t

​

+  

rs

−3t

​

=−  

rs

6t

​

 or

=−  

Coefficient of x  

2

 

Coefficient of x

​

=−  

r  

2

s  

2

 

6rst

​

=−  

rs

6t

​

 

Product of zeroes =αβ=  

rs

−3t

​

×  

rs

−3t

​

=  

r  

2

s  

2

 

9t  

2

 

​

 or  

=  

Coefficient of x  

2

 

Constant term  

​

=  

r  

2

s  

2

 

9t  

2

 

​

 

So, the relationship between the zeroes and the co

Step-by-step explanation: