OBJECTIVE TYPE Quin 0.35 has four c...
Question

# OBJECTIVE TYPE Quin 0.35 has four choice (A),B),(C), D) out of which ONLY ONE is correct. 01 le equation x + +b= has distinct real roots and x2+2x+b=0 has only one to root testach one of the following is trud? (4) 6=9,220 B) b=0,2<0 (C)b>0,250

JEE/Engineering Exams
Maths
Solution
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( operatorname{tat} quad f(x)=x^{2}+a x+b ) [ g(x)=x^{2}+a|x|+b ] Equation ( g(x)=0 ) has only one solution tomerer it is seen that if ( alpha ) satisfies the equ then ( -alpha ) alsodoes as well . [ begin{array}{l} therefore alpha=-alpha Rightarrow alpha=0 end{array} ] The root of ( g(x)=0 ) is 0 [ 0^{2}+a^{2}left|0^{0}right|^{2}+b=0 ] [ therefore b=0 ] ( therefore g(x)=x^{2}+a|x| ) [ =|x|^{2}+a|x|=|x|(|x|+a) ] If ( g(x)=0 ) either ( |x|=0 ) or ( |x|+a=0 ) Sunce o is the only nomible solution, ageqslanto lemence observe that if ( a=0 ) (2) ( f(x)=x^{2}, ) thich does not han ( therefore quad ) AM り ( quad a>0, b=0 ) ( Rightarrow ) Option ( (A) )