Question

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

Answer 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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