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Question
The divisor and quotient of the number 6123 are same and the remainder is half the divisor. Find the divisor.
Solution
Dividend = 6123
Now, divisor and quotient are same
Let divisor = quotient = d
Now, remainder = `1/2xxx=x/2`
Since dividend = divisor * quotient + remainder, we have
`6123= d^2+d/2`
∴12246= 2d2+d
∴2d2+d-12246 = 0
Comparing with ax2+bx+c, we get
a= 2, b= 1, c=-12246
`therefore d=(-b+-sqrt(b^2-4ac))/(2a)`
`=(-1+-sqrt(1^2-4(2)(-12246)))/4`
`=(-1+-sqrt97969)/4`
`=(-1+-313)/4`
∴`d=(-1+313)/4 or d=(-1-313)/4`
∴d= 78 or d= -78.5
Ignoring the negative value, the divisor is 78.
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