write a quadratic polynomial sum of whose zeroes is 2 and product is-8
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Given: Sum fo zeroes = (α+β)=8
Product of the zeroes = αβ=12
Required quadratic polynomial is
x
2
−(α+β)x+αβ=x
2
−(8)x+12
Now , find the zeroes of the above polynomial.
Let f(x)=x
2
−(8)x+12
= x
2
−6x−2x+12
=(x−6)(x−2)
Substitute f(x)=0
(x−6)=0 or (x−2)=0
⇒x=6 or x=2
2 and 6 are the zeroes of the polynomial .
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