Question

A two digits number is such that the product of the digits is 12 when 36 is added to the number the digits interchange their places. formulate the quadratic equation whose root(s) is (are) digit(s) of the number.​

Answer 1

Aɴsᴡᴇʀ

Let the ten's digit of the number be x

and it is given that the product of digits is 12

➪ unit's digit = 12/x

➪ number = 10x + 12/x

if 36 is added to the number the digits interchange their places.

$\bold{: \implies10x + \frac{12}{x} + 36 = 10 \times \frac{12}{x} + x } \\ \\ \bold{ : \implies 10x + \frac{12}{x} + 36 = \frac{120}{x} + x } \: \: \: \: \: \: \: \: \\ \\ \bold { : \implies 9x - \frac{108}{x} + 36 = 0 } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \bold{ : \implies 9 {x}^{2} - 108 + 36x = 0 } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ : \implies\bold{9( {x}^{2} - 12 + 4x) = 0 } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \bold{ : \implies \boxed{ \bold{ {x}^{2} + 4x - 12 = 0} }}\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

now we get the equation

• x² + 4x - 12 = 0

___________________________

form of a quadratic equation;

• ax² + bx + c = 0 (where a ≠ 0)

now, compare the equation to ax² + bx + c

then,

• a = 1
• b = 4
• c = -12

hence, required quadratic equation is x² + 4x - 12 = 0