Question

(a^2+b^2)x^2-2 (ac+bd)x+(c^2+d^2)=0 if ad=bc

Answer 1

$roots \: are \: equal \\ then \: \\ {b}^{2} - 4ac = 0 \\ {( - 2ac - 2bd)}^{2} - 4( {a}^{2} + {b}^{2} )( {c}^{2} + {d}^{2} ) = 0 \\ 4 {a}^{2} {c}^{2} + 4 {b}^{2} {d}^{2} + 8abcd - 4 {a}^{2} {c}^{2} - 4 {b}^{2} {c}^{2} - 4 {a}^{2} {d}^{2} - 4 {b}^{2} {d}^{2} = 0 \\ - 4( {b}^{2} {c }^{2} + {a}^{2} {d}^{2} - 2abcd) = 0 \\ {(bc - ad)}^{2} = 0 \\ bc = ad$