1f p(x)=2x³+ ax²- 11x + b is exactly divisible by (x – 2) and (x – 3), then the values of a and b are?​

1 thought on “1f p(x)=2x³+ ax²- 11x + b is exactly divisible by (x – 2) and (x – 3), then the values of a and b are?​”

1. Answer:

   P(x) = 2x³ + ax² – 11x + b

   P(x) is exactly divisible by x-2

   So, x-2 = 0

   x= 2

   also, p(x) =0

   putting the value of x in p(x)

   we get,

   2(2)³ + a(2)² – 11*2 + b = 0

   16 + 4a – 22 + b = 0

   4a + b -6 = 0

   4a + b = 6 ……………..(1)

   Now we have,

   P(x) is exactly divisible by x-3

   So, x-3 = 0

   x = 3

   also p(x) = 0

   putting the value of x in p(x)

   we get,

   2(3)³ + a(3)² – 11*3 + b = 0

   54 + 9a – 33 + b = 0

   9a + b + 21 = 0

   9a + b = -21 ……………(2)

   Solving eqn (1) and (2)

   Subtracting,

   4a + b = 6

   9a + b = -21

   (-) (-) (+)

   – 5a = 27

   a = – 5.4

   putting this value in (1)

   we get

   4 * (-) + b = 6

   -108/5 + b = 6

   -108/5 + b = 6b = 6 + 21.6

   b = 27.6

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