Question

If x = 2 & x = 0 are two roots of the polynomial f(x) = 2x³ - 5x² + ax + b. Find the values of and b. 

Answer 1

f(x) = 2(2)³ - 5(2)² + a(2) + b = 0 

⇒ 16 - 20 + 2a + b = 0 

⇒ 2a + b = 4     ....(i) 

⇒ f(0) = 2(0)³ - 5(0)² + a(0) + b = 0 

⇒ b = 0 

 So, 2a = 4 

 Hence, a = 2, b = 0