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प्रश्न
If ax2 + bx + c = 0 has equal roots, then c =
विकल्प
\[\frac{- b}{2a}\]
\[\frac{b}{2a}\]
\[\frac{- b^2}{4a}\]
\[\frac{b^2}{4a}\]
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उत्तर
The given quadric equation is ax2 + bx + c = 0 , and roots are equal
Then find the value of c.
Let `alpha = beta `be two roots of given equation
Then, as we know that sum of the roots
`alpha + beta = (-b)/ a`
`alpha + alpha = (-b)/ a`
`2alpha = (-b)/ (2a)`
`alpha = (-b)/ (2a)`
And the product of the roots
`alpha. beta = c/a`
`alpha alpha = c / a`
Putting the value of `alpha`
`(-b)/(2a) xx (-b)/(2a) = c/a`
`b^2/4a = c`
Therefore, the value of `c = (b^2)/(4a)`.
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