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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
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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
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
Answered by Thiyagarajan K | 07 Mar, 2019, 10:32: AM

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