Question

find the value of a and b px= x^4-5x³+4x²+ax+b and x-1 or x-2 are the factors of px​

Answer 1

Answer:

a = 8,  b = - 8

Step-by-step explanation:

As x - 1 and x - 2 are root of the given equation it must satisfy all the condition which x satisfies. So, when x = 1, and x = 2, value of polynomial is 0.

   For x = 1,

⇒ x^4 - 5x^3 + 4x^2 + ax + b = 0

⇒ (1)⁴ - 5(1)³ + 4(1)² + a(1) + b = 0

⇒ 1 - 5 + 4 + a + b = 0

⇒ b = - a

     For x = 2,

⇒ (2)⁴ - 5(2)³ + 4(2)² + a(2) + b= 0

⇒ 16 - 40 + 16 + 2a + b = 0

⇒ 2a + b = 8

⇒ 2a - a = 8

⇒ a = 8

        Hence, b = - a = - 8