Question

a two digit numbers is such that the product of the digits is 12. when 36 is added to the number the digits interchanging their Places. formulate the quadratic equation whose root(s) is (are) digit(s) of the number.

Answer 1

digits are  - 2 and -6  or 6 and 2

quadratic equation  i

s y^2 - 4y -12 = 0

Step-by-step explanation:

let dgts are x and y

according to qu = xy =12  or x = 12/y

10x + y + 36 = 10y + x

10x-x + y -10 y +36 =0

9x - 9 y = -36

x- y = -4

12/y -y = -4

12 -y^2 = -4 y

12 - y^2 + 4y =0

y^2 - 4y -12 = 0

y^ 2- 6y + 2y -12 =0

y(y-6) + 2 ( y-6) = 0

(y-6)(y+2) =0

so y = 6 or y = -2

so x= -2 or x= 6