Question

If the roots of the equation (a² + b²) x² – 2(ac + bd) x + (c² + d²) = 0 are equal, prove that `a/b = c/d`

Answer 1

(a² + b²) x² − 2 (ab + cd) x + (c² + d²) = 0

roots are equal so, D = b² − 4ac = 0

{2(ab + cd)}² −4 (a² + b²) (c² + d²) = 0

4(ab + cd)² −4 (a² + b²) (c² + d²) = 0

(a²b² + c²d² + 2abcd) −a²c²⁻a²d²⁻b²d² −b²c² = 0

−a²c² − b²d² + 2abcd = 0

−(a²c² + b²d² − 2abcd) = 0

{(ac − bd)²} = 0

ac − bd = 0

ac = bd

`a/b=d/c`