Q1 of 90 Page 2

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

t2 – 15

Let f(x) = t2 – 15


Now, if we recall the identity


(a2 – b2) = (a – b)(a + b)


Using this identity, we can write


t2 – 15 = (t – √15) (x + √15)


So, the value of t2– 15 is zero when t = √15 or t = – √15


Therefore, the zeroes of t2– 15 are √15 and – √15.


Verification


Now,


Sum of zeroes = α + β = √15 + ( – √15) = 0 or



Product of zeroes = αβ = (√15)( – √15) = – 15 or



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


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