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  • If   then the roots of the equation <img alt="x^{2}+2ax+a^{2}-b^{2}-c^{2}=0" src="/latex-image/

If  a,b,c\: \epsilon \: R then the roots of the equation x^{2}+2ax+a^{2}-b^{2}-c^{2}=0 are

Option: 1

Both real


Option: 2

Both imaginary


Option: 3

One real , one imaginary


Option: 4

Can't say


Answers (1)

best_answer

Coefficient are real , so nature of roots depend on D

D=b^{2}-4ac\\

     =\left ( 2a \right )^{2}-4\cdot 1\cdot \left ( a^{2}-b^{2}-c^{2} \right )\\

     =4a^{2}-4\left ( a^{2}-b^{2}-c^{2} \right )\\

     = 4\left (a^{2}- a^{2}+b^{2}+c^{2} \right )\\

     = 4\left ( b^{2}+c^{2} \right )

Clearly D\geq 0

          \Rightarrow both roots are real

Posted by

vinayak

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