Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • Engineering
  • Tell me? - Complex numbers and quadratic equations - JEE Main-5

If roots of ax^{2}+2bx+b= 0 are imaginary \left ( Where\: a\neq 0,\; a,b\epsilon R \right )  then roots of equation bx^{2}+\left ( b-c \right )x+\left ( b-c-a \right )=0 are \left ( c\, \epsilon \, R \right )

  • Option 1)

    real and distinct

  • Option 2)

    real and equal

  • Option 3)

    Imaginary

  • Option 4)

    one real, one imaginary

 

Answers (1)

best_answer

\because first equation has imaginary roots, so 

4b^{2}-4ab< 0\: \Rightarrow \: b^{2}-ab< 0\cdots \cdots \left ( 1 \right )

D of 2nd equation will be

D=\left ( b-c \right )^{2}-4b\left ( b-c-a \right )

\Rightarrow \: D=b^{2}+c^{2}-2bc-4b^{2}+4bc+4ab

\Rightarrow \: D=b^{2}+c^{2}+2bc+4\left ( ab-b^{2} \right )

\Rightarrow \: D=\left (b+c \right )^{2}+4\left ( ab-b^{2} \right )

                       \geq 0                   +ve

\therefore D is positive, So roots are real and Distinct

\therefore Option (A)

 

Complex Roots with non - zero Imaginary part -

D= b^{2}-4ac< 0

- wherein

ax^{2}+bx+c= 0

is the quadratic equation

 

 


Option 1)

real and distinct

This is correct

Option 2)

real and equal

This is incorrect

Option 3)

Imaginary

This is incorrect

Option 4)

one real, one imaginary

This is incorrect

Posted by

Himanshu

View full answer

JEE Main high-scoring chapters and topics

Study 40% syllabus and score up to 100% marks in JEE

Similar Questions

Trending Articles/News

anam-khan

JAC Chandigarh Counselling 2025: Round 1 seat allotment result out for BTech admissions
anam-khan

JoSAA round 5 seat allotment result 2025 out on josaa.nic.in
anam-khan

BTech aspirant from north-east or UT? Apply for CSAB NEUT counselling 2025 today

Latest Question