Question

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

Answer 1

Answer:

Step-by-step explanation:

since roots are equal, b² - 4ac = 0

4(ac+bd)² - 4(a²+b²)(c²+d²) = 0

a²c²+ b²d²+2abcd = a²c²+ b²d²+a²d²+b²c²

a²d² + b²c² - 2abcd = 0

(ad - bc)² = 0

ad = bc

a/b = c/d

= R.H.S

Hence proved.