Q1 of 90 Page 2

Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients:

x2 – 3

Let f (x) = x2 – 3


Now, if we recall the identity


(a2 – b2) = (a – b)(a + b)


Using this identity, we can write


x2 – 3 = (x – √3) (x + √3)


So, the value of x2 – 3 is zero when x = √3 or x = – √3


Therefore, the zeroes of x2 – 3 are √3 and – √3.


Verification


Now,


Sum of zeroes = α + β = √3 + ( – √3) = 0 or



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



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


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