If the equation ax^2+bx+c=0 and 5x^2+12x+13=0 have a common root , where a ,b and c are the sides of a triangle ABC , then

Answers (1)

Solution:   Since , equation 5x^2+12x+13=0 has imaginary roots 

    Hence , equation ax^2+bx+c=0 and 

   5x^2+12x+13=0  have both common roots 

  \ \ 	herefore hspace2cmfraca5=fracb12=fracc13=k(say)\ \ Rightarrow hspace2cma^2+b^2=25k^2+144k^2=(13k)^2=c^2\ \ Rightarrow hspace2cma^2+b^2=c^2

  Rightarrow           ABC is right angled triangle.

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