Question

In the polynomial p (x) = x² + ax + b p (3 + √2 )= 0, p (3 – √2 ) = 0, write this polynomial after finding a and b.

Answer 1

p (x) = x² + ax + b

p(3 + √2) = 0, (x – 3 – √2) is a factor (1) 

p(3 – √2 ) = 0, ( x – 3 + √2) is a factor (1) 

p(x) = x + ax + b = (x – 3 – √2) (x – 3 + √2)

 = (x – 3)² – ( √2)² (1) 

x² + ax + b = x – 6x + 7 (1)