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?

Dear rupali,

 the roots will be real and distinct 

the solution is attached

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jitender

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).