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iv) A two digit number is 5 times the sum of its digits and is also equal to 5 more
than twice the product of its digits. Formulate the quadratic equation to find the
number.
Ans: Let the digit at the ten's place be x and units place be y.
Then the number = 10x + y
According to the given conditions
10x + y = 5(x + y) (i)
10x + y = 5 + 2xy (ii)
(i) 10x + y = 5x + 5y
5x = 4y

Put this value of y in (ii), we have

2
40x + 5x = 20 + 10x
2
45x = 20 +10x
2
10x - 45x + 20 = 0
2
2x - 9x + 4 = 0
Which is the required equation.

Example 2 : Check whether the following are quadratic equations.
3
2
3
(i) x - 4x - x + 1 = (x - 2)
2
3
3
2
Ans: x - 4x - x + 1 = x - 8 - 6x + 12 x
2
2
-4x + 6x - x - 12x + 1 + 8 = 0
2
2x - 11x + 9 = 0
Since, the degree of the equation is 2, therefore, it is a quadratic
equation.
(ii) (x + 2)(2x - 3) = 2(x - 2)(x + 5)
Ans: (x + 2)(2x - 3) = 2(x - 2)(x + 5)
2
2
2x + x - 6 = 2(x + 3x - 10)
x - 6 = 6x - 20
5x - 14 = 0
Degree of equation is 1.So, it is not a quadratic equation.
(iii)

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