Q. 164.4( 30 Votes )

Find a quadratic

Answer :

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


= x2 – (sum of zeroes)x + product of zeroes


= x2 – ( – 2)x + ( – 3)


= x2 + 2x – 3


Verification


Sum of zeroes = α + β = 1 + ( – 3) = – 2 or



Product of zeroes = αβ = (1)( – 3) = – 3 or



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

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