Question

Find the quadratic polynomial , the sum of whose zeroes is 0 and the product of the zeroes is 2.
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Answer 1

Step-by-step explanation:

Given : Sum fo zeroes =  (α+β)=0

Product of the zeroes = αβ=−1

Required quadratic polynomial is  

x  

2

−(α+β)x+αβ=x  

2

−(0)x−1

=x  

2

−1

Now, find the zeroes of the above polynomial.

Let f(x)=x  

2

−1

= x  

2

−1  

2

 

=(x−1)(x+1)

Substitute f(x)=0  

(x−1)=0 or (x+1)=0  

⇒x=1 or x=−1

1 and −1 are the zeroes of the polynomial.

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