Question

solve the following ​

Answer 1

ANSWER :- a = 2 , b = -1

x² - 1 = ( x + 1 ) ( x - 1 )

x +1

ax³ + x² - 2x + 6

p(-1) ===> a(-1)³ + (-1)² - 2(-1) + b = 0

===> -a +1 +2 +b = 0

===> -a + b +3 = 0

===> a -b = 3 --------------(1)

( x - 1 )

p(+1) ===> a (1)³ + (1)² - 2(1) + b = 0

===> a + 1 -2 + b = 0

===> a + b -1 = 0

===> a + b = 1 ---------------(2)

a - b = 3 -------------(1)

a + b = 1 --------------(2)

(1)+(2)

==> 2a = 4

a = 2

a + b = 1

2 + b = 1

b = -1