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  • Try this! - Complex numbers and quadratic equations - JEE Main-5

ax^{2}+bx+c= 0\; \left ( Where \; a,b,c\, \epsilon \, I \right ) and x^{2}+5x+2= 0 have a common root then a:b:c equals

  • Option 1)

    1:2:5

  • Option 2)

    1:3:5

  • Option 3)

    1:5:2

  • Option 4)

    1:1:1

 

Answers (1)

x^{2}+5x+2=0  has irrational roots and both equations one given to have common root.Since a,b,c\; \epsilon \; Q\; \; so\; \; ax^{2}+bx+c=0   to satisfy condition of common root, it will have both roots common.

So, \frac{a}{1}=\frac{b}{5}=\frac{c}{2}\Rightarrow a:b:c=1:5:2

 

Condition for both roots common -

\frac{a}{{a}'}=\frac{b}{{b}'}=\frac{c}{{c}'}
 

- wherein

ax^{2}+bx+c=0 &

a'x^{2}+b'x+c'=0

are the 2 equations

 

 


Option 1)

1:2:5

This is incorrect

Option 2)

1:3:5

This is incorrect

Option 3)

1:5:2

This is correct

Option 4)

1:1:1

This is incorrect

Posted by

subam

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