If the polynomial ax3 +bx2 - c is divisible by x2 + bx +c then ab =?
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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
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Answer:
If the polynomial ax3 +bx2 - c is divisible by x2 + bx +c then ab =? If f(x) is divisible by g(x), then the “remainder” of a long division would equal zero.
hope this helps you mate
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