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IF a,b,c are real numbers satisfying the condition a+b+c =0 then the nature roots of the quadratic equation 3ax^2+5bx+c=0?

IF a,b,c are real numbers satisfying the condition a+b+c =0 then the nature roots of the quadratic equation 3ax^2+5bx+c=0?

Grade:

2 Answers

jitender lakhanpal
62 Points
9 years ago

Dear rupali,

 the roots will be real and distinct 

the solution is attached

 

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1409_36248_quadratic equation.JPG

Ashwin Muralidharan IIT Madras
290 Points
9 years ago

Hi Rupali,

 

The discriminant of the QE is,

 

D = 25b2 - 12ac = 25(-a-c)2 - 12ac = 25a2+25c2+50ac-12ac = 25a2+25c2+38ac

   = 6a2+6b2+19a2+19c2+38ac = 6a2+6b2+19(a+c)2 -------- (which is always poitive, as they are square terms)

 

As D > 0, the roots of this QE are always real and distinct.

 

Hope that helps.

 

All the best.

Regards,

Ashwin (IIT Madras).

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