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Coordinate Geometry
Question
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Find the values of a and b so that (x + 1) and (x - 1) are factors of x4 + ax3 - 3x2 + 2x + b.  

Answer

Let p (x) = x4 + ax3 - 3x2 + 2x + b
If (x + 1) and (x - 1) are factors of p(x), then by factor theorem,
p(-1) = 0 ...(1) | x + 1 = 0 ⇒ x = -1
and    p(1) = 0 ...(2) | x - 1 = 0 ⇒ x = 1
Now,
P(-1) = 0
⇒ (-1)4 + a(-1)3 - 3(-1)2 + 2 (-1) + b = 0
⇒ 1 - a - 3 - 2 + b = 0
⇒    -a + b = 4    ...(3)
and    p(1) = 0
⇒ (1)4 + a(1)3 - 3(1)2 + 2 (1) + b = 0
⇒ 1 + a - 3 + 2 + b = 0
⇒    a + b = 0    ...(4)
Solving (3) and (4), we get
a = -2,b = 2

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Some More Questions From Coordinate Geometry Chapter

Which of the following expressions are polynomials in one variable and which are not? State reasons for your answer.

4x2 - 3x + 7

Which of the following expressions are polynomials in one variable and which are not? State reasons for your answer.

x10+ y3 + t50

Write the coefficients of x2 in each of the following:

2 + x2 + x

Write the coefficients of x2 in each of the following:
2 - x2 + x3