13.If the polynomial fx) ax + bx - c is divisible by the polynomial g(

1.	13.If the polynomial fx) ax + bx - c is divisible by the polynomial g()+bxthen find the value of ab.
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 = 2bc=2b/ac = 2b/(1/b).......substituting value of aor c = 2b2...........

13.If the polynomial fx) ax + bx - c is divisible by the polynomial g()+bxthen find the value of ab.

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 = 2bc=2b/ac = 2b/(1/b).......substituting value of aor c = 2b2...........