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

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`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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