Prove that the rots of the following equations are real
[1] x2 - 2ax + a- b2 - c2 = 0
[2] (a - b + c)*x2 + 4(a- b)*x +(a- b -c) = 0
?

Dear student, 

Let us first prove it for the equation.

x2 - 2ax +a2 - b2 - c2 = 0We have, A = 1; B= -2a; C = a2-b2-c2Now, D = B2 - 4AC = -2a2 - 41a2-b2-c2 = 4b2+c2 0Since, D0, the roots of the given equation will be always real.

We can use similar method to solve question number 2 as well.

Regards

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