Given that (x + 2) and (x + 3) are factors of 2 3 + a 2 + 7 − , find a and b.
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f x + 2 is a factor of 2x3 + ax2 + 7x – b, then x + 2 = 0 x = - 2 in equation
2(- 2)3 + a(- 2)2 + 7(- 2) – b = 0
2(- 8) + a(4) + 7(- 2) – b = 0
-16 + 4a – 14 – b = 0
4a – b = 30 …(1)
Also given that x + 3 is a factor of
2x3 + ax2 + 7x – b, then x + 3 = 0
x = - 3 in equation2(- 3)3 + a(- 3)2 + 7(- 3) – b = 0
2(- 27) + a(9) + 7(- 3) – b = 0
- 54 + 9a – 21 – b = 0
9a – b = 75 ….(2)
Solving (1) and (2), we get
a = 9, b = 6
Step-by-step explanation:
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