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Try this! - Algebra - JEE Main

If the equations x^{2}+2x+3=0\; and\; ax^{2}+bx+c=0,a,b,c\; \epsilon R, have a common root, then a : b : c is :

 

 

  • Option 1)

    3 : 1 : 2

  • Option 2)

    1 : 2 : 3

  • Option 3)

    3 : 2 : 1

  • Option 4)

    1 : 3 : 2

 
Answers (2)
135 Views
N neha

As we have learned

Quadratic Expression Graph when a > 0 & D < 0 -

No Real and Equal root of

f\left ( x \right )= ax^{2}+bx+c

& D= b^{2}-4ac

- wherein

 

 

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

 

 For x^2+2x+3=0

Discriminant = 4-12 = -8 < 0 

Both the roots are common as complex roots occur in conjugate \therefore a:b:c= 1:2:3

 

 


Option 1)

3 : 1 : 2

Option 2)

1 : 2 : 3

Option 3)

3 : 2 : 1

Option 4)

1 : 3 : 2

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