Question

LEVEL-2 EXAMPLE 5 If x = 2 and x = 0 are roots of the polynomial f(x) = 2x - 5x^2 + ax + b. Find the values of a and b. ​

Answer 1

Answer:

Step-by-step explanation:

Let f ( x ) = 2x³ - 5x² + ax + b = 0

If x = 2 is the root of the polynomial f ( x ) , then

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

⇒2 ( 8 ) - 5 ( 4 ) + 2a + b = 0

⇒ 16 - 20 + 2a + b = 0

⇒ - 4 + 2a + b = 0

⇒ 2a + b = 4 --------eq ( 1 ) (say ).

If x = 0 is the root of the polynomial f ( x ), then

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

⇒ 2 ( 0 ) - 5 ( 0 ) + 0 + b = 0

⇒ 0 - 0 + 0 + b = 0

⇒ b = 0

On substituting ,

2a + b = 4

⇒ 2a + 0 = 4

⇒ 2a = 4

⇒ a = 4/2

⇒ a = 2

∴ The values of a and b are 2 and 0.