Question

Pls answer this question

Answer 1

Answer:

10a + 4b = 9

Step-by-step explanation:

  Using remainder theorem:

When, it is divided by x - 2, remainder = 0. So when x = 2, polynomial is equal 0.

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

 ⇒ 5 + 2b - 2( 4 ) + a( 8 ) = 0

 ⇒ 5 + 2b - 8 + 8a = 0

 ⇒ 8a + 2b - 3 = 0

 ⇒ 8a + 2b = 3

Similarly, when x = - 1, polynomial is equal to 0.

⇒ 5 + b( - 1 ) - 2( - 1 )^2 + a( - 1 )^3 = 0

⇒ 5 - b - 2( 1 ) + a( - 1 ) = 0

⇒ 5 - b - 2 - a = 0

⇒ 3 - b - a = 0

⇒ a + b = 3

⇒ 2a + 2b = 6

      Adding both results:

⇒ ( 8a + 2b ) + ( 2a + 2b ) = 3 + 6

⇒ 8a + 2b + 2a + 2b = 9

⇒ 8a + 2a + 2b + 2b = 9

⇒ 10a + 4b = 9

  Proved.