Solve the following questions 
1. if p and q are roots of the quadratic equation x^2-(alpha-2)x-alpha-1=0, then what is the minimum  value of p^2+q^2?
 
2.If the difference of roots of the quadratic equation x^2+4px+p=0 is same as the difference of roots of quadratic equation x^2+4px+q=0,then find the relation between p and q if p!=q.
 
3.if x^2+5x+6+k=0,then the value of for which roots of the given equation differ by 1 is
 
4.if b=0,c <0 in ax^2+bx+c=0,then find the value of X. 

Asked by nitinkumarsingh.singh.75 | 28th Jul, 2015, 11:12: AM

Expert Answer:

C o n s i d e r space t h e space g i v e n space e q u a t i o n comma x squared minus open parentheses alpha minus 2 close parentheses x minus alpha minus 1 equals 0 A l s o space g i v e n space t h a t space p space a n d space q space a r e space r o o t s space o f space t h e space q u a d r a t i c space e q u a t i o n. therefore p plus q equals fraction numerator negative open square brackets negative open parentheses alpha minus 2 close parentheses close square brackets over denominator 1 end fraction equals open parentheses alpha minus 2 close parentheses p q equals fraction numerator negative open parentheses alpha plus 1 close parentheses over denominator 1 end fraction equals negative open parentheses alpha plus 1 close parentheses W e space k n o w space t h a t comma p squared plus q squared equals open parentheses p plus q close parentheses squared minus 2 p q rightwards double arrow p squared plus q squared equals open parentheses alpha minus 2 close parentheses squared minus 2 open square brackets negative open parentheses alpha plus 1 close parentheses close square brackets rightwards double arrow p squared plus q squared equals open parentheses alpha minus 2 close parentheses squared plus 2 open square brackets open parentheses alpha plus 1 close parentheses close square brackets rightwards double arrow p squared plus q squared equals alpha squared plus 4 minus 4 alpha plus 2 alpha plus 2 rightwards double arrow p squared plus q squared equals alpha squared minus 2 alpha plus 6 rightwards double arrow p squared plus q squared equals alpha squared minus 2 alpha plus 1 plus 5 rightwards double arrow p squared plus q squared equals open parentheses alpha minus 1 close parentheses squared plus 5 T h u s comma space p squared plus q squared space i s space m i n i m u m space i f space alpha equals 1. T h u s comma space p squared plus q squared space i s space m i n i m u m space i f space alpha equals 1 space a n d space t h e space m i n i m u m space v a l u e space i s space 5

Answered by Vimala Ramamurthy | 29th Jul, 2015, 11:11: AM

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