Question

Find the value of a and b so that x+1 and x-1 are factors of x4+ax3+2x2-3x+B

Answer 1

Ans:- Given:-

p(x) = x⁴+ax³+2x²-3x+b

g(x) = (x+1) and (x-1)

to find, value of a and b

Solution:-

=> x + 1= 0

=> x = -1

now, put the value of x in p(x)

=> p(-1) = (-1)⁴+a(-1)³+2(-1)²-3(-1)+b = 0

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

=> p(-1) = 6-a+b = 0 -----------(1)

=> x - 1 = 0

=> x = 1

now, put the value of x in p(x)

=> p(1) = (1)⁴+a(1)³+2(1)²-3(1)+b = 0

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

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

from(1) and (2) we get,

=> 6 - a + b = a + b ( since both are equal to 0)

=> -a - a = -6

=> -2a = -6

=> a = 3

now, put the value of a in (2) we get

=> a + b = 0

=> 3 + b = 0

=> b = -3

here is your answer

hope it will help you