Question

please solve sum no-11 right, i mark him as brilliantlist

Answer 1

Answer:

x^4-2x³+3x²-ax+b is divided by x-1 and x+1

so, first let p(x) = x-1 = 0 ==> x = 1

so, put value of x in polynomial

==> (1)^4-2(1)³+3(1)²-a(1)+b = 5 (because remainder is 5 )

==> 1 - 2 + 3 - a + b = 5

==> 2 - a+ b = 5

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

given :- when divide its polynomial by x+1 then 19 remainder is left

==> x+1 ==> x = -1

put value again in polynomial

==> (-1)^4-2(-1)³+3(-1)²-a(-1) + b = 19

==> 1 + 2 + 3 + a + b = 19

==> a + b = 19-6

==> a+b = 13 ....(2)

from eq(1) and (2)

-a+b = 3

a+b = 13

==> 2b = 16

==> b = 8

putting value of b in eq(1)

-a+b = 3

-a+8 = 3

==> -a = -5

==> a = 5

so, putting value of a and b in polynomial

x^4-2x³+3x²-ax+b

==> x^4-2x³+3x²-5x+8

so, now we divide x^4-2x³+3x²-5x+8 by  x-2

p(x) = x-2 ==> x = 2

putting value of x in polynomial x^4-2x³+3x²-5x+8

x^4-2x³+3x²-5x+8

==> (2)^4-2(2)³+3(2)²-5(2)+8

==> 16 - 16 + 12 - 10 + 8

==> 20-10

===> 10

thanks for giving question