Question

if (x-1)and (x-2 are the factors of x^4-px^2+q then the value of √p+√q

Answer 1

Answer:

The value of √p + √q = 2 + √5

Step-by-step explanation:

Let P(x) = x⁴ - px² + q

Since (x-1) is a factor

Remainder  P(1) = 0            [by remainder Thm]

               1 -p + q = 0  

                  p - q = 1    . . . . . . . (1)

Since (x-2) is a factor

Remainder P(2) = 0

              16 - 4p + q = 0  

                     4p -q = 16  . . . . . . . (2)  

(2) - (1)

3p = 15 ⇒ p = 5

From (1)     5 - q = 1 ⇒    q = 4    

∴ √p + √q = √5 + √4 = 2 + √5