a two digit number is such that the product of its digits is 12 when 36 is added to this number the digits interchange their places find the number
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Step-by-step explanation:
Let the ten's digit of the number be x
It is given that the product of digits is 12
Then unit's digit=
x
12
Given number can be written as =10x+
x
12
If 36 is added to the number the digits interchange their places
∴10x+
x
12
+36=10×
x
12
+x
⇒10x−x−
x
120−12
+36=0
⇒9x−
x
108
+36=0
⇒9x
2
+36x−108=0
⇒x
2
+4x−12=0 (divided throughout by 9)
hence, required quadratic equation is x
2
+4x−12=0
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