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algebra
problem on time and work solved as a quadratic


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algebra

Person A takes 6 days less than the time taken by the person
B to finish a particular piece of work. If both A and B work
together , they can finish it in 4 days. Find the time that B
 would take to finish this work by himself

Let x be number of days taken by person B to finish
the work by himself
therefore A takes (x-6) days to finish the work by
himself.

therefore [1 / (x-6)] and [1/x] are the part of the work
finished by A and B  respectively in a single day

Working together they require 4 days to finish the work
therefore

4{
[1 / (x-6)] + [1/x] } = 1

4{ x + (x-6)}/{x(x-6)} =1

4{ 2x -6)}/{x(x-6)} =1

4{ 2x -6)} = {x(x-6)}
8x-24 = (x^2) -6x
(x^2) - 14x + 24 = 0
factorising
(x-2)(x-12) = 0
x=2 or x=12

if x = 2, y =2-6 = -4 is negative which
is not possible

therefore x = 12 days.
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form a quadratic equation whose roots are
3 and 4

sum of the roots S = 3 +4 =7

product of the roots P = 3*4 = 12

required quadratic equation is


(x^2) -Sx+P=0
(x^2) -7x + 12=0

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