CBSE Class 11-science Answered
questions 6
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Asked by sohailsidmd002 | 11 Oct, 2020, 14:35: PM
Part-(i)
x2 - px + q = 0
roots of the above quadratic equation are :- ![begin mathsize 14px style 1 half open parentheses p plus square root of p squared minus space 4 space q end root close parentheses space a n d space 1 half open parentheses p minus square root of p squared minus space 4 space q end root close parentheses end style](https://images.topperlearning.com/topper/tinymce/cache/1e37a718e83cff525eb2e723cc527351.png)
![begin mathsize 14px style 1 half open parentheses p plus square root of p squared minus space 4 space q end root close parentheses space a n d space 1 half open parentheses p minus square root of p squared minus space 4 space q end root close parentheses end style](https://images.topperlearning.com/topper/tinymce/cache/1e37a718e83cff525eb2e723cc527351.png)
Ratio of the roots :- ![begin mathsize 14px style fraction numerator p minus square root of p squared minus 4 q end root over denominator p plus square root of p squared minus 4 q end root end fraction space equals space 1 half end style](https://images.topperlearning.com/topper/tinymce/cache/1429ed16b15bff73e81fca68adb9ecea.png)
![begin mathsize 14px style fraction numerator p minus square root of p squared minus 4 q end root over denominator p plus square root of p squared minus 4 q end root end fraction space equals space 1 half end style](https://images.topperlearning.com/topper/tinymce/cache/1429ed16b15bff73e81fca68adb9ecea.png)
By cross multiplication and after simplification, we get , p2 = 9 ( p2 - 4 q ) or 2p2 = 9q or p2 = (9/2) q
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part - ( ii )
Given quadratic equation :- q x2 + p x + q = 0
if roots are imaginary, then we have , p2 - 4 q2 < 0 or p2 < 4 q2 or p < 2q
since p > 0 , we get the condition 0 < p < 2q
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part - ( iii )
if ax2 + bx + c = 0 has exactly one root x= 0 , then c = 0
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Part-(iv)
given quadratic equation :- 4x2 + 2bx + c = 0
if b = 0 , then 4x2 + c = 0
above equation has imaginary roots and they are , ![begin mathsize 14px style plus 1 half square root of negative c end root space space a n d space minus 1 half square root of negative c end root end style](https://images.topperlearning.com/topper/tinymce/cache/4a943e29719c04660fac04e2f7eda640.png)
![begin mathsize 14px style plus 1 half square root of negative c end root space space a n d space minus 1 half square root of negative c end root end style](https://images.topperlearning.com/topper/tinymce/cache/4a943e29719c04660fac04e2f7eda640.png)
Hence ratio of imaginary roots :- 1 : -1
Answered by Thiyagarajan K | 15 Oct, 2020, 09:37: AM
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