Question

If x-a is a factor of x3 - 3x²a + 2a²x + b, then the find value of b. -​

Answer 1

$= {x}^{3} - 3 {x}^{2} a + 2 {a}^{2} x + b$

$x - a = 0$

$x = a$

$= {a}^{3} - 3( {a)}^{2} + 2( {a)}^{2} + b$

$= {a}^{3} - 3 {a}^{2} + 2 {a}^{2} + b$

$= {a}^{3} - {a}^{2} + b$

$= {a}^{2} (a - 1 + b)$

$= a - 1 + b$

$- b = - a + 1$

$b = a + 1$

Answer 2

Answer:

Let f (x) = x³ - 3x²a + 2a²x + b

Since, x - a is a factor of f(x) then, f (a) = 0

⇒ a³ - 3a²a + 2a²a + b = 0  

⇒ a³ - 3a³ + 2a³ + b = 0  

⇒ -  2a³ + 2a³ + b = 0  

⇒ b = 0

Hence, the value of b is 0.