Question

If THE ROOTS OF QUADRATIC
EQUATION (a²+ b² x ²-2(ac + bd] x
+ c² + d ² = 0 ARE EQUAL , PROVE
that a/b=c/d​

Answer 1

Answer:

Given that the roots are equal so

D=0 that is

b²- 4ac=0

b² = 4ac

where a = a²+b²

b= -2(ac+bd)

c=c²+d²

so, {-2(ac+bd)}²=4(a²+b²)(c²+d²)

using identity (a+b)²=a²+2ab+b² 4a²c²+8acbd+4b²d²=4a²c²+4a²d²+4b²c²+4b²d²

[4a²c²,4b²d² get cancelled]

4a²d²+4b²c²-8acbd=0

taking 4 common

4(a²d²-8acbd+b²c²)=0

so,by identity

(ad-bc)²=0

taking square root at L.H.S and R.H.S

so now, ad-bc=0

ad=bc

a/b=c/d

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