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Question 1 (iv)
Find the zeroes of the following polynomials by factorization method and verify the relations between the zeroes and the coefficient of the polynomials
(iv) t32t215t


Solution

iv)  Let  f(t)=t32t215t+0.....(constant term is zero)
= t(t22t15)
= t(t25t+3t15)
= t[t(t5)+3(t5)]
= t(t5)(t+3)
 So, the value of t32t215t is Zero when t = 0 or t – 5 = 0 or t + 3 = 0
i.e.,  when t = 0 or t = 5  or t = - 3
so, the zeroes of t32t215t are 3,0 and 5
 sum of zeroes = 3+0+5=2=(2)1
= (1)(Coefficentoft2Coefficient of t3)
Sum of product of two zeroes at a time
= (3)(0)+(0)(5)+(5)(3)
= 0+015=15
= (1)2(Coefficient of tCoefficient of t3)
and product of zeroes (3)(0)(5)=0
= (1)3(Constant termCoeffidient of t3)
Hence, verified the relations between the zeroes and the coefficients of the polynomial.

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