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Question 1(i)
Find the zeroes of the following polynomials by factorization method and verify the relations between the zeroes and the coefficient of the polynomials
(i) 4x23x1

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Solution

Let f(x) = 4x23x1
= 4x24x+x1 [by splitting the middle term]
= 4x(x1)+1(x1)
= (x1)(4x+1)
So, the value of 4x23x1 is zero when x – 1 = 0 or 4x + 1 = 0 i.e., when x = 1 or x= 14
So, the zeroes of 4x23x1 are 1 and 14

Now to verify the relations between the zeroes and the coefficient:
Sum of zeroes = (ba)=114=34=(3)4
=(1)Coefficient of xCoefficient of x2.

And product of zeroes = (ca)=(1)(14)=(14)
= (1)2constant termCoefficient of x2
Hence, verified.

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