Question

If p and q are zeroes ofthe polynomial t²-4t + 3, show that 1/p +1/q -2pq + 14/3= 0

Answer 1

Hi ,

It is given that p , q are two zeroes of the

polynomial p( t ) = t² - 4t + 3

To find p and q we have take p( t ) = 0

t² - 4t + 3 = 0

t² - t - 3t + 3 = 0

t( t - 1 ) - 3( t - 1 ) = 0

( t - 1 )( t - 3 ) = 0

Therefore ,

t - 1 = 0 or t - 3 = 0

t = 1 or t = 3

p = 1 , q = 3

Now ,

1/p + 1/q - 2pq + 14/3

= 1/1 + 1/3 - 2 × 1 × 3 + 14/3

= 1 + 1/3 - 6 + 14/3

= - 5 + ( 1/3 + 14/3 )

= -5 + 15/3

= -5 + 5

= 0

Hence proved.

I hope this helps you.

: )

Answer 2

Answer:

p( t ) = t² - 4t + 3

polynomial p( t ) = t² - 4t + 3

To find p and q we have take p( t ) = 0

t² - 4t + 3 = 0

t² - t - 3t + 3 = 0

t( t - 1 ) - 3( t - 1 ) = 0

( t - 1 )( t - 3 ) = 0

Therefore ,

t - 1 = 0 or t - 3 = 0

t = 1 or t = 3

p = 1 , q = 3

Now ,

1/p + 1/q - 2pq + 14/3

= 1/1 + 1/3 - 2 × 1 × 3 + 14/3

= 1 + 1/3 - 6 + 14/3

= - 5 + ( 1/3 + 14/3 )

= -5 + 15/3

= -5 + 5

= 0

Hence proved.

HOPE IT HELP YOU