Pls solve this problem
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Answer:
a = 2, b = 9
Step-by-step explanation:
Let p(x) = 2t⁴ + 3t³ - at² - bt - 12
as p(x) is divisible by t² - 3
⇒ t² - 3 will be a factor of p(x).
Remainder obtained after dividing p(x) by t² - 3 should be 0.
Long Division Method:
t² - 3) 2t⁴ + 3t³ - at² - bt - 12
2t⁴ + 0t³ - 6t²
-------------------------------
3t³ + t²(-a+6) - bt - 12
3t³ + t² - 9t
-----------------------------------
t²(-a + 6) + t(-b + 9) - 12
t²(-a + 6) + 0t + 3a - 18
-------------------------------------------
t(-b + 9) + 3a - 6
∴ (-b + 9)t + 3a - 6 = 0
⇒ -b + 9 = 0 and 3a - 6 = 0
⇒ b = 9, a = 2
Therefore, a = 2 and b = 9
Hope it helps!
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