if alpha and beta are roots of ax2 + bx +c then prove that cx2 + bx + a has 1alpha and 1/beta as zeroes
Answer :
and are zeros of ax2 + bx + c , So from relationship between zeros and coefficient , we get
+ = ------------ ( 1 )
And
= ------------ ( 2 )
Now we divide equation 1 by equation 2 , we get
------------ ( 3 )
And
1 divide by equation 2 , we get
------------ ( 4 )
now from second equation cx2 + bx + a , we get
Sum of zeros = , From equation 3 , we get
Sum of zeros =
And
Product of zeros = , from equation 4 , we get
Product of zeros =
So, we can say that zeros of cx2 + bx + a are . ( Hence proved )
and are zeros of ax2 + bx + c , So from relationship between zeros and coefficient , we get
+ = ------------ ( 1 )
And
= ------------ ( 2 )
Now we divide equation 1 by equation 2 , we get
------------ ( 3 )
And
1 divide by equation 2 , we get
------------ ( 4 )
now from second equation cx2 + bx + a , we get
Sum of zeros = , From equation 3 , we get
Sum of zeros =
And
Product of zeros = , from equation 4 , we get
Product of zeros =
So, we can say that zeros of cx2 + bx + a are . ( Hence proved )