Question

Pls solve this problem
....

Answer 1

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!