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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