Question

Find the quadratic polynomial whose zeros are 1/3 and -1​

Answer 1

Answer:

Step-by-step explanation:

Let the zeroes of the quadratic polynomial be α=1,β=−3

Then, α+β=1+(−3)=−2

αβ=1×(−3)=−3

Sum of zeroes =α+β=−2

Product of zeroes =αβ=−3

Then, the quadratic polynomial =x  

2

−( sum of zeroes )x+ product of zeroes =x  

2

−(−2)x+(−3)=x  

2

+2x−3

Verification:

Sum of zeroes =α+β=1+(−3)=−2 or  

=−  

Coefficient of x  

2

 

Coefficient of x

​

=−  

1

(2)

​

=−2

Product of zeroes =αβ=(1)(−3)=−3 or  

=  

Coefficient of x  

2

 

Constant term  

​

=  

1

−3

​

=−3

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