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

(v) 2x2+72x+34

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Solution

v) Let f(x)=2x2+72x+34=8x2+14x+3
= 8x2+12x+2x+3
= 4x(2x+3)+1(2x+3)
= (2x+3)(4x+1)
So, the value of 8x2+14x+3 is zero when 2x + 3 = 0 or 4x + 1 = 0
i.e., when x= 32 or x = 14
so, the zeroes of 8x2+14x+3 are 32 and 14
sum of zeroes = 3214=74=72×2
= (Coefficient of x)(Coefficient of x2)
And product of zeroes = (32)(14)=38=32×4
= Constant termCoefficient of x2
Hence, verified the relations between the zeroes and the coefficients of the polynomial.

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