if the polynomial ax3+bx-c is divisible by x2+bx+c find the value of a and b

Asked by katyalaanchal | 31st May, 2011, 12:00: AM

Expert Answer:

If f(x) is divisible by g(x), then the "remainder" of a long division would equal zero.

The remainder after dividing f(x) by g(x) is

[(ab² - ac + b)x + c(ab - 1)]/(x² + bx + c)

For the numerator to equal zero, both terms in parentheses have to be equal to zero

ab² - ac + b = 0 and ab - 1 = 0

ab = 1.......(i)

or a=1/b

 
 

ab² - ac + b = 0

ac = ab² + b

ab = 1...........(from (i))

ac = b + b = 2b
 
c=2b/a
 
c = 2b/(1/b).......substituting value of a
 
or c = 2b2

Answered by  | 1st Jun, 2011, 04:57: PM

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