questions 6

Asked by sohailsidmd002 | 11th Oct, 2020, 02:35: PM

Expert Answer:

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
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
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
Hence ratio of imaginary roots :- 1 : -1 

Answered by Thiyagarajan K | 15th Oct, 2020, 09:37: AM