Question

if A and b are the roots of equation X^2 - px + q then write the values of 1 by a + 1 by b​

Answer 1

a and b are roots of quadratic equation x² - px + q.

Now , we have to find out the value of (1/a )+ (1/b)

We can write (1/a )+ (1/b) as :-

$\tt\implies \: \dfrac{1}{a} + \dfrac{1}{b} = \dfrac{a + b}{ab}.....(1)$

Which means ,

(1/a )+ (1/b) = (sum of roots)/(product of roots)

Now , for x² - px + q product of roots = q/1

=> product of roots = q

And sum of roots = -(-p)/1

=> sum of roots = p

Now put a+b = p and ab = q in equation (1) :-

$\tt \implies\dfrac{a + b}{ab} = \dfrac{p}{q}$

$\tt\implies \: \dfrac{1}{a} + \dfrac{1}{b} = \dfrac{p}{q}$

Answer :

• p/q