Question

Find the values of a and b such that the polynomial $x^3-a{x}^2$ - bx + 4 has (x - 1) and (x + 1) as factors

• A. a = 4 b = 5
• B. a = 1 b = 4
• C. a = 5 b = 2
• D. a = 3 b = 4

Answer 1

The correct option is B

a = 1

b = 4

(x - 1) is a factor of given polynomial $x^3-a{x}^2-bx+4$

$\Rightarrow (1{)}^3-a(1{)}^2$ - b + 4 = -0 [x - 1 = 0 $\Rightarrow$ x = 1]

1 - a - b + 4 = 0

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

(x + 1) is a factor of the given polynomial.

$(-1{)}^3-a(-1{)}^2$ -b (-1) + 4 = 0 [x + 1 = 0, x = -1]

-1 - a + b + 4 = 0

- a + b = -3 -------- (2)

On solving both the equations,

a = 1 and b = 4