Find a quadratic polynomial, the sum and product of whose
zeroes are 0 and -V2 respectively. Hence find the zeroes.
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Step-by-step explanation:
Answer
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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