PUMPA - SMART LEARNING
எங்கள் ஆசிரியர்களுடன் 1-ஆன்-1 ஆலோசனை நேரத்தைப் பெறுங்கள். டாப்பர் ஆவதற்கு நாங்கள் பயிற்சி அளிப்போம்
Book Free DemoConsider the equation \(ax^2 + bx + c = 0\), where \(a \ne 0\).
The roots of the quadratic equation are and .
If \(\alpha\) and \(\beta\) are the roots of a quadratic equation \(ax^2 + bx + c = 0\), then:
\(\alpha =\) and \(\beta =\)
Sum of the roots \(=\) \(\alpha + \beta\)
\(=\) \(+\)
\(=\)
\(=\)
Sum of the roots \(=\) \(\alpha + \beta\) \(=\)
Product of the roots \(=\) \(\alpha \beta\)
\(=\) \(\times\)
\(=\)
\(=\)
\(=\)
\(=\)
Product of the roots \(=\) \(\alpha \beta\) \(=\)
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, \( x^2 - (\text{sum of roots}) x + \text{product of roots} = 0\).
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