Q1 of 90 Page 2

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

x2 – 2x – 8

Let f(x) = x2 – 2x – 8


By splitting the middle term, we get


f(x) = x2 – 4x + 2x – 8 [∵ – 2 = 2 – 4 and 2×4 = 8]


= x(x – 4) + 2(x – 4)


= (x + 2) (x – 4)


On putting f(x) = 0, we get


(x + 2) (x – 4) = 0


⇒ x + 2 = 0 or x – 4 = 0


⇒x = – 2 or x = 4


Thus, the zeroes of the given polynomial x2 – 2x – 8 are – 2 and 4


Verification


Sum of zeroes = α + β = – 2 + 4 = 2 or



Product of zeroes = αβ = ( – 2)(4) = – 8 or



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


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