Question

if a and b are roots of the equation x2-px+q =0 , then write value of 1/a+1/b

Answer 1

doed see
if a and b are roots of the given playnomial
then
a+b=-b/a
=-(-p)
=p
ab=c/a
=q
Now we will find
1/a+1/b
=a+b/ab
=p/q
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Answer 2

The value of $\dfrac{1}{a}+\dfrac{1}{b}$ is $\dfrac{-p}{q}$.

Explanation:

The given quadratic equation is :

$x^2-px+q=0$

The roots of this equation are a and b.

For a quadratic equation, the sum of roots is given by :

sum of roots = $\dfrac{-b}{a}$

$a+b=\dfrac{-b}{a}=\dfrac{p}{1}=-p$.........(1)

For a quadratic equation, the product of roots is given by :

Product of roots = $\dfrac{c}{a}$

$ab=\dfrac{c}{a}=q$.........(2)

Dividing equation (1) and (2) we get :

$\dfrac{a+b}{ab}=\dfrac{-p}{q}\\\\\dfrac{1}{a}+\dfrac{1}{b}=\dfrac{-p}{q}$

So, the value of $\dfrac{1}{a}+\dfrac{1}{b}$ is $\dfrac{-p}{q}$.

Learn more,

Quadratic equation

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