The quardatic Equation whose roots are the reciprocal of the roots of the equation _ - ?

Question

#ax^2 + bx + c = 0#

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Answer 1 · 2018-08-03T07:42:25

The reqd. quadratic eqn.is :
#cx^2+bx+a=0#

Let #alpha and beta # be the roots of the quadratic eqn.

#ax^2+bx+c=0#

#:.alpha+beta=-b/a and alpha*beta=c/a#

The reciprocal of the roots of this eqn. are : #1/alpha and 1/beta#

So, the quadratic eqn. whose roots are #1/alpha and 1/beta# is :

#x^2-(1/alpha+1/beta)x+1/alpha*1/beta=0#

#=>x^2-((alpha+beta)/(alpha*beta))x+1/(alpha*beta)=0#

#=>x^2-((-b/a)/(c/a))x+1/(c/a)=0#

#=>x^2+b/cx+a/c=0#

#=>cx^2+bx+a=0#