Question

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

Answer 1

Answer:

proved below

Step-by-step explanation:Zeroes are p & q

Sum of zeroes = p+q = -(-4)/1 = 4

Product of zeroes = pq = 3

1/p + 1/q - 2pq + 14/3 =0

p+q/qp - 2pq +14/3 = 0

Lets insert above given values

4/3-2*3 + 14/3 = 0

4-18/3 +14/3 = 0

-14/3 +14/3 = 0

Answer 2

Let, $p(t) = t^2 - 4t + 3$ where $p, \ q$ are its zeroes.

So, $p + q = - \dfrac{b}{a} = - \dfrac{(-4)}{1} = 4$

And $pq = \dfrac{c}{a} = \dfrac{3}{1} = 3$.

Now,

$\dfrac{1}{p} + \dfrac{1}{q} - 2pq = - 14/3$

{to be proved}

LHS:-

$\dfrac{1}{p} + \dfrac{1}{q} - 2pq$

= $\dfrac{p + q}{pq} - 2(pq)$

= $\dfrac{4}{3} - 2(3)$

= $\dfrac{4}{3} - 6$

= $\dfrac{4-18}{3}$

= $- \dfrac{14}{3}$

RHS:-

$- \dfrac{14}{3}$

Therefore, LHS = RHS.