Prove that the equation `x^2(a^2+b^2)+2x(a c+b d)+(c^2+d^2)=0` has no real root, if `a d!=b c`.

Explanation

We know

Discriminant,
`D=4(ac+bd)^2−4(a^2+b^2)(c^2+d^2)`

`D=4[(ac+bd)^2−(a^2+b^2)(c^2+d^2)]`

`D=4[a^2c^2+b^2d^2+2acbd−a^2c^2−a^2d^2−b^2c^2−b^2d^2]`

`D=4[2acbd−a^2d^2−b^2c^2]`

`D=−4[a^2d^2+b^2c^2−2adbc]`

`D=−4(ad−bc)^2`

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