CBSE Class 11-science Answered
let the equations be x^2+x+2=0 and ax^2+bx+1=0 have atleast one common root then a+b equals to
Asked by sandeepkumarbhadauria41 | 15 Sep, 2021, 14:52: PM
Given equations are
x2 + x + 2 = 0 ...........................(1)
a x2 + b x + 1 = 0 ........................(2)
Roots of Eqn.(1) :-
![begin mathsize 14px style fraction numerator negative 1 plus-or-minus square root of 1 minus 8 end root over denominator 2 end fraction end style](https://images.topperlearning.com/topper/tinymce/cache/9fae9b64142bc4bf4ae0ff261f019052.png)
Roots of Eqn.(2) :- ![begin mathsize 14px style space fraction numerator negative b space plus-or-minus space square root of b squared space minus space 4 a end root over denominator 2 a end fraction space end style](https://images.topperlearning.com/topper/tinymce/cache/a26124d6ac9162d3dec77126f625c731.png)
![begin mathsize 14px style space fraction numerator negative b space plus-or-minus space square root of b squared space minus space 4 a end root over denominator 2 a end fraction space end style](https://images.topperlearning.com/topper/tinymce/cache/a26124d6ac9162d3dec77126f625c731.png)
if both equations have a common root , then -b/(2a) = -1/2 or b = a
Also ![begin mathsize 14px style fraction numerator b squared over denominator 4 a squared end fraction minus 1 over a space equals space minus 7 over 4 end style](https://images.topperlearning.com/topper/tinymce/cache/df6a66ea94f4d7bf40ca3185353eff2e.png)
![begin mathsize 14px style fraction numerator b squared over denominator 4 a squared end fraction minus 1 over a space equals space minus 7 over 4 end style](https://images.topperlearning.com/topper/tinymce/cache/df6a66ea94f4d7bf40ca3185353eff2e.png)
if we substitute b =a in above expression, we get a = (1/2) after simplification
Hence we have , a = b = 1/2 or a+b = 1
Answered by Thiyagarajan K | 20 Sep, 2021, 21:50: PM
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