Thrice the square of a natural number decreased by four

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Thrice the square of a natural number decreased by four times the number is equal to 50 more than the number. The number is:

1. 4
2. 5
3. 10
4. 6

Correct Option: B

Let the number be x.
According to the question,
3 × x² – 4 × x = x + 50
⇒ 3x² – 5x – 50 = 0
⇒ 3x² – 15x + 10x – 50 = 0
⇒ 3x (x – 5) + 10 (x – 5) = 0
⇒ (x – 5) (3x – 10) = 0

⇒ x = 5 or	−10
	3

But the number is natural.

∴ x ≠	−10
	3

Hence, the required number = 5.