Question

In a number system, the product of 44 and 11 is 3414. the number 3111 of this system when converted into the decimal number system becomes

Answer 1

Answer:

Explanation:

44*11 = 484

Let 3414 be in base x

Converting 3414 from base x to decimal and equating it to 44*11.

3x³ + 4x² + x + 4 = 484

3x³ + 4x² + x - 480 = 0

(x-5)(3x² + 19x + 96) = 0

The above equation has only one real root = 5

Therefore the unknown base of 3414 is 5.

(3111) base 5 = (3*5³ + 1*5² + 1*5 +1) base 10

=(125*3 + 25+5+1)

= (406) base 10