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Answer :
Let the number of articles produced be \(x\).
Thus, the cost of production of each article can be expressed as \(2x + 3\).
As the total cost of production on that day is 90 Rs.,
\(\Rightarrow x(2x + 3) = 90\)
\(\Rightarrow 2x^2 + 3x - 90 = 0\)
(Splitting 3x as -12x + 15x )
\(\Rightarrow 2x^2 + -12x +15x - 90 = 0\)
\(\Rightarrow 2x(x - 6) + 15(x - 6) = 0\)
\(\Rightarrow(2x + 15)(x - 6) = 0\)
The roots of this equation are the values of x for which \((2x + 15)(x - 6) = 0 \)
which are,
\(2x + 15 = 0 \) or \(x - 6 = 0\)
Thus, \(x = \frac{-15}{2}\) or \(x = 6\)
Since the number of articles produced cannot be a negative number, \(x = \frac{-15}{2}\) is rejected.
Thus, the number of articles produced is 6 and the cost of each article is \(2×6 + 3\) = 15Rs.