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  • Need clarity, kindly explain! - Complex numbers and quadratic equations - JEE Main

If  a,b,c,d\; \epsilon \; R  there are two equations ax^{2}+bx+c= 0 , ax^{2}+dx-c= 0  such that a\neq 0 then

  • Option 1)

    Both equations will have real roots

  • Option 2)

    Both equations will have imaginary roots

  • Option 3)

    One will have real roots and other will have imaginary roots 

  • Option 4)

    At least one will have real roots 

 

Answers (1)

best_answer

D_{1}=b^{2}-4ac

D_{2}=d^{2}+4ac

D_{1}+D_{2}= b^{2}+d^{2}\geqslant 0

This is possible when at least one of D_{1} & D_{2} is non negative, So at least one will have real roots.

 

System of quadratic equations. -

If  ax^{2}+bx+c= 0  and  px^{2}+qx+r= 0  have discriminants  D_{1}  &  D_{2}  such that D_{1}+D_{2}\geq 0  then atleast one quadratic has real roots  \left ( a,b,c,p,q,r\epsilon R \right )

-

 

 


Option 1)

Both equations will have real roots

This is incorrect

Option 2)

Both equations will have imaginary roots

This is incorrect

Option 3)

One will have real roots and other will have imaginary roots 

This is incorrect

Option 4)

At least one will have real roots 

This is correct

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Plabita

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