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Question 1 (i)
For each of the following, find a quadratic polynomial whose sum and product of the zeroes respectively are as given. Also, find the zeroes of these polynomials by factorization.
i) 83,43

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Solution

(i) given that, sum of zeroes (S) = 83
and product of zeroes (P) = 43
Required quadratic expression, f(x)=x2Sx+P
=x2+83x+43=3x2+8x+4
Using factorization method
3x2+6x+2x+4
=3x(x+2)+2(x+2)=(x+2)(3x+2)
Hence, the zeroes of f(x) are – 2 and 23

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