Simple addition of remainders or what?

Algebra Level 3

Let p ( x ) p(x) be a polynomial which when divided by ( x − 19 ) (x-19) gives a remainder of 91 and when divided by ( x − 91 ) (x-91) gives a remainder of 19. 19. Find \the remainder, when p ( x ) p(x) is divided by ( x − 19 ) ( x − 91 ) (x-19)(x-91) .

72 x+72 x-110 x-72 6x+88 110-x

Rishik Jain by Rishik Jain , 21, India

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

1 solution

Rishik Jain
Jan 5, 2016

Given : p ( 19 ) = 91 \textbf{Given :} p(19) = 91 and p ( 91 ) = 19 p(91) = 19

p ( x ) = ( x − 19 ) ( x − 91 ) + a x + b p(x) = (x-19)(x-91) +ax+b

p ( 19 ) = 19 a + b p(19) = 19a+b

19 a + b = 91 19a+b=91

p ( 91 ) = 91 a + b p(91) = 91a+b

91 a + b = 19 91a+b=19

Thus we get 2 equations in 2 variables. ∴ a = − 1 , b = 110 \therefore a=-1 , b=110

The remainder is a x + b ax+b . 110 − x \large \boxed{110 - x}

1 Helpful 0 Interesting 0 Brilliant 0 Confused

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...