The divisor and qutient of the number 6123 are same andthe remainder is half of the divisor. Find the divisor.
To find the divisor, we need to understand the relationship between the divisor, quotient, and remainder in a division problem.
Let's say a number N is divided by a divisor D, resulting in a quotient Q and a remainder R. The relationship can be expressed as follows:
N = D * Q + R
In this case, we know that the divisor and the quotient are the same, and the remainder is half of the divisor. Let's represent the divisor/Q, and the remainder/R as variables to solve the equation.
So, the given information can be expressed as:
6123 = D * D + (D/2)
To solve this equation, we can rearrange it to a quadratic equation:
D^2 + (D/2) - 6123 = 0
Now we can solve this quadratic equation for D using various methods, such as factoring, completing the square, or using the quadratic formula. Let's use the quadratic formula to find the value of D:
D = (-b ± √(b^2 - 4ac)) / 2a
For our equation, the values are:
a = 1
b = 1/2
c = -6123
Plugging in these values, the formula becomes:
D = (-(1/2) ± √((1/2)^2 - 4 * 1 * -6123)) / (2 * 1)
Simplifying further:
D = (-1/2 ± √(1/4 + 24492)) / 2
D = (-1/2 ± √(24493/4)) / 2
D = (-1/2 ± √(6123.25)) / 2
Taking the positive square root:
D = (-1/2 + 78.326) / 2
D = 77.826 / 2
D ≈ 38.913
Therefore, the divisor of the number 6123 is approximately 38.913.
What is the square root of 6123?
6123/x = x + (1/2)x/x
times x
6123 = x^2 + (1/2)x
times 2
2x^2 + x - 12246 = 0
(x - 78)(2x + 157) = 0
x = 78 or x = -157
check:
6123/78 = 78 + remainder of 39 , which is 1/2 of 78
6123/-157 ≠ -157 + (????)
the divisor is 78