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Algebra

Hot goIITian

 Joined: 23 Apr 2012 Post: 163
3 Jul 2012 08:26:55 IST
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Engineering Entrance , JEE Main , JEE Advanced , Mathematics , Algebra

prove that two quadratic equations ax^2+bx+c=0 and 2x^2-3x+4=0 cannot have a common root unless 6a=-4b=3c

Blazing goIITian

Joined: 8 Oct 2008
Posts: 8064
6 Jul 2012 11:50:20 IST
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hello

Here the roots are non real for the second equation.

For a ,b,c to be real Than its both the roots must be common to the other given equation hence.

a/2=b/-3=c/4

Cool goIITian

Joined: 16 Aug 2011
Posts: 90
7 Jul 2012 11:46:58 IST
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see...for both the equation have a common root ...the curves of both the roots should intersect at a point...r8.but in the 2nd equation the roots are complex..and we know complex roots are conjugate to one another so for one root to be common the other root has to be common .... r8..sousing the condition of both roots to be commona/2=b/-3=c/4from there6a=-4b=3c...

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