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If a,b,c are in A.P then the roots of the equation ax^2+2bx+c=0 are
Asked by mbalvanthreddy3608 | 07 Mar, 2019, 06:21: AM
roots of the equation ( ax2 +bx +c) = 0 are ![begin mathsize 12px style fraction numerator negative b plus-or-minus square root of b squared space minus space 4 space a space c end root over denominator 2 a end fraction end style](https://images.topperlearning.com/topper/tinymce/cache/4174a558cd5539ad05130855ee69a1ea.png)
![begin mathsize 12px style fraction numerator negative b plus-or-minus square root of b squared space minus space 4 space a space c end root over denominator 2 a end fraction end style](https://images.topperlearning.com/topper/tinymce/cache/4174a558cd5539ad05130855ee69a1ea.png)
since a, b, c are in A.P., b = a+d and c = a + 2d , where d is the common difference
hence roots are ![begin mathsize 12px style fraction numerator negative open parentheses a plus d close parentheses plus-or-minus square root of open parentheses a plus d close parentheses squared minus 4 a open parentheses a plus 2 d close parentheses end root over denominator 2 space a end fraction space equals space space fraction numerator negative open parentheses a plus d close parentheses plus-or-minus square root of d squared minus 6 space a space d space minus space 3 space a squared end root over denominator 2 space a end fraction end style](https://images.topperlearning.com/topper/tinymce/cache/576b89f470749f474c1da8aac91ee56e.png)
![begin mathsize 12px style fraction numerator negative open parentheses a plus d close parentheses plus-or-minus square root of open parentheses a plus d close parentheses squared minus 4 a open parentheses a plus 2 d close parentheses end root over denominator 2 space a end fraction space equals space space fraction numerator negative open parentheses a plus d close parentheses plus-or-minus square root of d squared minus 6 space a space d space minus space 3 space a squared end root over denominator 2 space a end fraction end style](https://images.topperlearning.com/topper/tinymce/cache/576b89f470749f474c1da8aac91ee56e.png)
Answered by Thiyagarajan K | 07 Mar, 2019, 10:32: AM
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