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Question 1 (ii)
Find the zeroes of the following polynomials by factorization method and verify the relations between the zeroes and the coefficient of the polynomials
(ii) 3x2+4x4

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Solution

(ii) 3x2+4x4
Let f(x)=3x2+4x4
=3x2+6x2x4 [by splitting the middle term]
=(x + 2) (3x – 2)
So, the value of 3x2+4x4 is zero when x+2=0 or 3x – 2 = 0, i.e., when x=2 or x=23
so, the zeroes of 3x2+4x4 are 2 and 23
Sum of zeroes = 2+23=43
= (1)[Coefficient of xCoefficient of x2]
And product of zeroes = (2)(23)=43
=(1)2(Constant termCoefficient of x2)
Hence, verified the relations between the zeroes and the coefficients of the polynomial.

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