Question

find the product of zeros of a quadratic polynomial x^-2x-8​

Answer 1

Answer:

f(x)=x  

2

−2x−8

⇒f(x)=x  

2

−4x+2x−8

⇒f(x)=x(x−4)+2(x−4)]

⇒f(x)=(x−4)(x+2)

Zeros of f(x) are given by f(x) = 0

⇒x  

2

−2x−8=0

⇒(x−4)(x+2)=0

⇒x=4 or x=−2

So, α=4 and β=−2

∴ sum of zeros =α+β=4−2=2

Also, sum of zeros =  

Coefficient of x  

2

 

Coefficient of x

​  

 

=  

1

−(−2)

​  

=2

So, sum of zeros =α+β=−  

Coefficient ofx  

2

 

Coefficient of x

​  

 

Now, product of zeros =αβ=(4)(−2)=−8

Also, product of zeros =  

Coefficient ofx  

2

 

Constant term

​  

 

=  

1

−8

​  

=−8

∴ Product of zeros =  

Coefficient of x  

2

 

Constant term

​  

=αβ

Step-by-step explanation: