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Question

Find the zeros of the following polynomial by factorization method and verify the relations between the zeroes and the coefficient of the polynomials :
y2+325y5

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Solution

Let f(y)=y2+325y5

For zeroes of f(y),f(y)=0

y2+325y5=0

2y2+3.5y10=0

2y2+45y15y10=0

2y(y+25)5[y+25]=0

(y+25)(2y5)=0

y+25=0 or 2y5=0

y=25 or y=52

verification:
α=25,β=52,

a=1,b=325 and c=5

α+β=ba

25+52=3251

45+52=325

352=325

LHS=RHS

Hence, verified.

α.βca

(25)(52)=51

5=5

LHS=RHS

Hence, verified.

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