Quadratic Equation Solution8





In this page quadratic equation solution8 we are going to see solution of the word problems of the topic quadratic equation.

Question 14

A two digit number is four times the sum of its digits and twice the product of the digits. Find the number.

Solution:

Let "x y" be the required two digit number

x y = 4 (x + y)



Question 15

A two digit number such that the product of its digits is 21. When 36 is subtracted from the number the digits are interchanged. Find the number.

Solution:

Let "x y" be the required two digit number

A two digit number such that the product of its digits is 21

 x(y) = 21

   y = 21/x  ---- (1)

When 36 is subtracted from the number the digits are interchanged

 x y - 36 = y x

10 x + y - 36 = 10 y + x

10 x - x + y - 10 y = 36

 9 x - 9 y = 36

 Now we are going to divide the whole equation by 9,so we get

 x - y = 4  --- (2)

 Now we are going to apply the value of y that is first equation in the second equation.

            x - (21/x) = 4

         x² - 21  = 4 x

         x² - 4 x - 21 = 0

         x² - 7 x + 3 x - 21 = 0

   x (x - 7) + 3 (x - 7) = 0

 (x - 7) (x + 3) = 0

 x - 7 = 0             x + 3 = 0

 x = 7                     x = -3

To get he value of y we have to apply 7 instead of x in the first equation

          y = 21/x

          y = 21/7

          y = 3

Therefore the required two digit number is 73

Verification:

 A two digit number such that the product of its digits is 21

 7 (3) = 21

  21 = 21

When 36 is subtracted from the number the digits are interchanged

73 - 36 = 37

      37 = 37

quadratic equation solution8 quadratic equation solution8