if alpha and beta are roots of ax2 + bx +c then prove that cx2 + bx + a has 1alpha and 1/beta as zeroes

Answer :

α and  β are zeros of ax2 + bx + c  , So from relationship between zeros and coefficient , we get

α + β = -ba  ------------ ( 1 )

And

α  β = ca      ------------ ( 2 )

Now we divide equation 1 by equation 2 , we get

α + β αβ = -baca = -bc       ------------ ( 3 )

And

1 divide by equation 2 , we get

1αβ = 1ca = ac       ------------ ( 4 )

now from second equation  cx2 + bx + a , we get

Sum of zeros  = -bc  , From equation 3 , we get

Sum of zeros  = α + β αβ = 1α  + 1β  

And

Product of zeros  = ac , from equation 4 , we get

Product of zeros  = 1αβ 

So, we can say that zeros of cx2 + bx + a  are 1α  and 1β    .                               ( Hence proved )

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