Question

please solve this question ............

Answer 1

Answer:

a = 3, b = -3

Step-by-step explanation:

Let f(x) = 2x³ + ax² + bx - 2.

(i)

Since, (2x - 3) is a factor of f(x), f(3/2) = 0.

⇒ 2(3/2)³ + a(3/2)² + b(3/2) - 2 = 7

⇒ (27 + 9a + 6b)/4 = 9

⇒ 27 + 9a + 6b = 36

⇒ 9a +  6b - 9 = 0

⇒ 3a + 2b - 3 = 0    

⇒ 3a + 2b = 3

(ii)

Since, (x + 3) is a factor of f(x), f(-3) = 0

⇒ 2(-3)³ + a(-3)² + b(-3) - 2 = -20

⇒ 9a - 56 = 20 + 3b

⇒ 9a = 3b + 36

⇒ 9a - 3b - 36 = 0

⇒ 3a - b - 12 = 0

⇒ 3a - b = 12

On solving (i) & (ii), we get

3a + 2b = 3

3a - b = 12

-------------------

     3b = -9

       b = -3

Substitute b = -3 in (i), we get

⇒ 3a + 2b = 3

⇒ 3a + 2(-3) = 3

⇒ 3a - 6 = 3

⇒ a = 3

Therefore, the values are a = 3, b = -3.

Hope it helps!