Question

If the polynomial ax3 +bx2 - c is divisible by x2 + bx +c then ab =?

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Answer 1

Answer:

ab = 1

Step-by-step explanation:

• 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

Answer 2

Hey Buddy

Here's The Answer

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Let

f(x) = ax³ + bx² - c

g(x) = x² + bx + c

Given f(x) is divisible by g(x), which means remained is 0

So,

=> ( ax³ + bx² - c )/( x² + bx + c ) = 0

By the attachment we got the result

=> ( ab² - ac + b )x + ( ab - 1 ) = 0

==> We get two equations

==> x( ab² - ac + b) = 0

=> ab² - ac + b = 0____( 1 )

==> c( ab - 1 = 0 )

=> ab - 1 = 0_______( 2 )

Now from ( 2 )

=> ab = 1 ✓

Hope It Helps

:)