Let `a , ba n dc`be the three sides of a triangle, then prove that the equation `b^2x^2+(b^2=c^2-alpha^2)x+c^2=0`has imaginary roots.

Let `a , ba n dc`be the three sides of a triangle, then prove that the

1.	Let `a , ba n dc`be the three sides of a triangle, then prove that the equation `b^2x^2+(b^2=c^2-alpha^2)x+c^2=0`has imaginary roots.
Answer» `b^(2) x^(2) + (b^(2) + c^(2) - a^(2)) x + c^(2) = 0` Let `f(x) = b^(2) x^(2) + (2 bc cos A) x + c^(2) = 0` Also in `Delta ABC`, where `A in (0, pi)` in a triangle, we find `cos A in (-1, 1)`. Now, `D = (2bc cos A)^(2) - 4b^(2) c^(2) = 4b^(2) c^(2) (cos^(2) A - 1) lt 0` Hence, the roots are imaginary

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Let `a , ba n dc`be the three sides of a triangle, then prove that the equation `b^2x^2+(b^2=c^2-alpha^2)x+c^2=0`has imaginary roots.

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