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  • Tell me? - Complex numbers and quadratic equations - JEE Main-18

If equations

ax^{2}+bx+c=0,\left ( a,b,c\epsilon R,a\neq 0 \right )and 2x^{2}+3x+4= 0

Have a common root ,then a:b:c equals :

  • Option 1)

    1:2:3

  • Option 2)

    2:3:4

  • Option 3)

    4:3:2

  • Option 4)

    3:2:1

 

Answers (2)

best_answer

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

 

 2x^2+3x+4=0  has determinant = 9-32 = -23 < 0 

So , non real roots which means both roots are common (as complex roots occurs in conjugate )

So, a:b:c = 2:3:4

 

 

 


Option 1)

1:2:3

Option 2)

2:3:4

Option 3)

4:3:2

Option 4)

3:2:1

Posted by

Himanshu

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