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Theory:

Consider the equation \(ax^2 + bx + c = 0\), where \(a \ne 0\).
 
The roots of the quadratic equation are b+b24ac2a and bb24ac2a.
 
If \(\alpha\) and \(\beta\) are the roots of a quadratic equation \(ax^2 + bx + c = 0\), then:
 
\(\alpha =\) b+b24ac2a and \(\beta =\) bb24ac2a
 
Sum of the roots \(=\) \(\alpha + \beta\)
 
\(=\) b+b24ac2a \(+\) bb24ac2a
 
\(=\) b+b24acbb24ac2a
 
\(=\) 2b2a=ba
Sum of the roots \(=\) \(\alpha + \beta\) \(=\) ba
Product of the roots \(=\) \(\alpha \beta\)
 
\(=\) b+b24ac2a \(\times\) bb24ac2a
 
\(=\) bb+bb24ac+b24acb+b24acb24ac2a×2a
 
\(=\) b2+bb24acbb24acb24ac4a2
 
\(=\) b2b2+4ac4a2
 
\(=\) 4ac4a2=ca
Product of the roots \(=\) \(\alpha \beta\) \(=\) ca
Since \((x - \alpha)\) and \((x - \beta)\) are factors of \(ax^2 + bx + c = 0\):
 
\((x - \alpha) (x - \beta) = 0\)
 
\(\Rightarrow x^2 - \alpha x - \beta x + \alpha \beta = 0\)
 
\(\Rightarrow x^2 - (\alpha + \beta) x + \alpha \beta = 0\)
 
\(\Rightarrow x^2 - (\text{sum of roots}) x + \text{product of roots} = 0\)
If \(\alpha\) and \(\beta\) are the roots of a quadratic equation, then the general formula to construct the quadratic equation is \(x^2 - (\alpha + \beta) x + \alpha \beta = 0\).
 
That is, \( x^2 - (\text{sum of roots}) x + \text{product of roots} = 0\).