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Prove that the roots of the equation x^2 - 2ax + a^2 - b^2 - c^2 = 0 are real , (a, b, c € R).

Prove that the roots of the equation x^2 - 2ax + a^2 - b^2 - c^2 = 0 are real , (a, b, c € R).

Grade:11

1 Answers

Arun
25763 Points
2 years ago
Dear Ananya
 
first we find D
 
D = 4a^2 – 4(a^2 – b^2 – c^2)
 
 = 4 a^2 – 4a^2 + 4b^2 + 4c^2
 
 = 4b^2 + 4c^2
 
always positive
 
hence roots are real 

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