Most Important Selected Qs for JEE AdvancedMathematicsQuadratic Equation
Consider, f(x)=x^2+ x+a^2+a+1 , where a, R . Identify correct statement(s) about f(x) .
Options
- ALeast positive integral value of for which f(x)=0 has real roots for some real value of ' a ' is 2
- BIf =2 then set of values of a for which f(x)=0 has real roots is [-1,0]
- CIf both the roots of the equation f(x)=0 and 2 x^2-x+6=0 are identical then sum of all possible values of ' a
- DIf f(1+x)=f(1-x) x R , then =2
Correct answer
C. If both the roots of the equation f(x)=0 and 2 x^2-x+6=0 are identical then sum of all possible values of ' a
Step-by-step solution
(1) aligned & D 0 ^2-4 (a^2+a+1 ) 0 ^2 4 [ (a+ 1 2 )^2+ 3 4 ] & ^2 3 3 aligned (2) For =2D=4-4 (a^2+a+1 ) 0 a [-1,0] (3) 1 2 = -1 = a^2+a+1 6 a^2+a-2=0 (a+2)(a-1)=0 a=-2,1 (4) -b 2 a =1= - 2 =-2