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Hence a=-23 and b=38
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p(x) = 2x³ - 3x² + ax + b
Here, x = 2, 3
p(2) = 2(2)³ - 3(2)² + a(2) + b
0 = 16 - 12 + 2a + b
0 = 4 + 2a + b ________(1)
p(3) = 2(3)³ - 3(3)² + a(3) + b
0 = 54 - 27 + 3a + b
0 = 27 + 3a + b _______(2)
(2) - (1)
0 = 27 + 3a + b
- ( 0 = 4 + 2a + b )
=> 0 = 23 + a
Therefore, a = - 23
Then,
0 = 4 + 2a + b
0 = 4 + 2(-23) + b
0 = 4 - 46 + b
42 = b
Hope it helps
p(x) = 2x³ - 3x² + ax + b
Here, x = 2, 3
p(2) = 2(2)³ - 3(2)² + a(2) + b
0 = 16 - 12 + 2a + b
0 = 4 + 2a + b ________(1)
p(3) = 2(3)³ - 3(3)² + a(3) + b
0 = 54 - 27 + 3a + b
0 = 27 + 3a + b _______(2)
(2) - (1)
0 = 27 + 3a + b
- ( 0 = 4 + 2a + b )
=> 0 = 23 + a
Therefore, a = - 23
Then,
0 = 4 + 2a + b
0 = 4 + 2(-23) + b
0 = 4 - 46 + b
42 = b
Hope it helps
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