Q1 of 90 Page 2

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

x2 + 7x + 10

Let f(x) = x2 + 7x + 10


By splitting the middle term, we get


f(x) = x2 + 5x + 2x + 10 [∵ 7 = 2 + 5 and 2×5 = 10]


= x(x + 5) + 2(x + 5)


= (x + 2) (x + 5)


On putting f(x) = 0 , we get


(x + 2) (x + 5) = 0


⇒ x + 2 = 0 or x + 5 = 0


⇒x = – 2 or x = – 5


Thus, the zeroes of the given polynomial x2 + 7x + 10 are – 2 and – 5


Verification


Sum of zeroes = α + β = – 2 + ( – 5) = – 7 or



Product of zeroes = αβ = ( – 2)( – 5) = 10 or



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


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