Question

if alpha and bita are the zeros of p(x) = x²-px+q then 1/alpha + 1/bita is equal to​

Answer 1

Consider the given polynomial

f(x)=

x 2

px+ q

α and β are the zeros of given polynomial

We know that,

Sumofzeros=−

cofficentofx

2

cofficentofx

α+ β=

1

−(−p)

α+ β= p

Productofzeros=

cofficentofx

2

constant

α× β=

1

q

α× β= q

Then,

Part (1):-

α 2

β 2

(α+β) 2

2αβ

α 2

β 2

p 2

2q

Part (2):-

α

1

+

β

1

=

αβ

α+β

=

q

p

Hence, this is the answer.

Thank u for asking

Answer 2

Answer:

alpha + beta/alphabeta

=p/q