2. Questions Bank
  3. 10th Class
  4. Mathematics
  5. Quadratic Equations

10th Class Mathematics Quadratic Equations Question Bank Quadratic Equations

  • question_answer
    If the roots of the equation               \[({{a}^{2}}+{{b}^{2}}){{x}^{2}}-2b(a+c)x+({{b}^{2}}+{{c}^{2}})=0\] are equal, then _____.                  

    A)  \[2b=a+c\]               

    B)                    \[{{b}^{2}}=ac\]                            

    C)                     \[b=\frac{2ac}{a+c}\]         

    D)                    \[b=ac\]      

    Correct Answer: B

    Solution :

    Since roots of the given equation are equal   \[\therefore \]\[D=0\] \[\Rightarrow \] \[{{(-2b(a+c))}^{2}}-4({{a}^{2}}+{{b}^{2}})({{b}^{2}}+{{c}^{2}})=0\] \[\Rightarrow \] \[4{{b}^{2}}({{a}^{2}}+{{c}^{2}}+2ac)-4({{a}^{2}}{{b}^{2}}+{{a}^{2}}{{c}^{2}}+{{b}^{4}}\]                                                  \[+{{b}^{2}}{{c}^{2}})=0\]                                        \[\Rightarrow \]\[{{a}^{2}}{{b}^{2}}+{{b}^{2}}{{c}^{2}}+2a{{b}^{2}}c-{{a}^{2}}{{b}^{2}}-{{a}^{2}}{{c}^{2}}-{{b}^{4}}-{{b}^{2}}{{c}^{2}}=0\] \[\Rightarrow \]\[2a{{b}^{2}}c-{{a}^{2}}{{c}^{2}}-{{b}^{4}}=0\]\[\Rightarrow \]\[{{b}^{4}}+{{a}^{2}}{{c}^{2}}-2a{{b}^{2}}c=0\] \[\Rightarrow \]\[{{({{b}^{2}}-ac)}^{2}}=0\] \[\Rightarrow \] \[{{b}^{2}}=ac\]


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