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Question

If roots the equation x2(1+m2)+2 mc x+c2a2=0 are equal, then find c.

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Solution

Given,

(1+m2)x2+2mcx+(ca2)=0

since the roots are equal

b2=4ac

(2mc)2=4(1+m2)(c2a2)

4m2c2=4(c2a2+m2c2m2a2)

0=c2a2m2a2

c2=a2(1+m2)

c=a1+m2

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