Find the value of (k/2)^{2} if x^{4} + x^{3} – kx^{2} – 18 gives remainder 0 when divided by (x + 3).

- 1
- 2
- 3
- 4

Option 4 : 4

**Given :**

x^{4} + x^{3} – kx^{2} -18 gives remainder 0 when divided by (x + 3).

**Calculations :**

Put x + 3 = 0 or x = -3 in the equation

x^{4} + x^{3} – kx^{2} -18 = 0 at x = -3

⇒ (-3)^{4} + (-3)^{3} – k(-3)^{2} – 18 = 0

⇒ 81 – 27 – 9k -18 = 0

⇒ 9k = 36

⇒ k = 4

⇒ k/2 = 2

So,

⇒ (k/2)^{2} = 2^{2}

⇒ 4

**∴ The correct choice will be option 4**

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