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  • I need help with - Complex numbers and quadratic equations - JEE Main-2

If  p,q,r,s\; \epsilon \; R  then the equation \left ( x^{2}+px+s \right )\left ( x^{2}+qx+s \right )\left ( x^{2}+rx-2s \right )= 0 have

  • Option 1)

    two real roots

  • Option 2)

    4 real roots

  • Option 3)

    six real roots

  • Option 4)

    at least two real roots

 

Answers (1)

best_answer

D_{1}=p^{2}-4s;\, D_{2}=q^{2}-4s;\, D_{3}=r^{2}+8s

D_{1}+D_{2}+D_{3}=p^{2}+q^{2}+r^{2}\geqslant 0

\Rightarrow at least one of D_{1},D_{2}\: and\: D_{3} is non-negative so at least one factor will have real roots, so at least two real roots are there.

\therefore Option (D)

 

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)

two real roots

This is incorrect

Option 2)

4 real roots

This is incorrect

Option 3)

six real roots

This is incorrect

Option 4)

at least two real roots

This is correct

Posted by

Aadil

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