2. Sample Papers
  3. JEE Main & Advanced

JEE Main & Advanced Sample Paper JEE Main Sample Paper-40

  • question_answer
    If 2a + 3b + 6c = 0 then at least one root of the equation \[a{{x}^{2}}+bx+c=0\]lies in the interval

    A) (0,1)                

    B) (1,3) 

    C) (2,3)                            

    D) (1,2)

    Correct Answer: A

    Solution :

    Let \[f(x)=a{{x}^{2}}+bx+c\] \[g(x)\int_{{}}^{{}}{f(x)=\frac{a{{x}^{3}}}{3}+\frac{b{{x}^{2}}}{2}+cx}\] \[\therefore \]\[g(1)=\frac{a}{3}+\frac{b}{2}+c=2a+3b=c=0\] \[g(0)=0=g(1)\] \[\therefore \]g(x) is continuous apply Rolle's theorem \[\Rightarrow \]g(x) = 0 for some value \[x\in (0,1)\Rightarrow g'(x)=f(x)=a{{x}^{2}}+bx+c=0\]has a root in (0, 1)


You need to login to perform this action.
You will be redirected in 3 sec spinner