Question

If alpha and beta are root of equation 5x2-7x+1=0 find value of 1/ alpha + 1/beta

Answer 1

Given :

The quadratic equation is   5 x² - 7 x + 1 = 0

alpha and beta are roots of this equation

To Find :

The value of   $\dfrac{1}{\alpha }$  +  $\dfrac{1}{\beta }$

Solution :

From standard quadratic equation

i.e    a x² + b x + c = 0

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

The products of its roots = $\dfrac{c}{a}$

Now, compare given equation with standard equation

 As α , β is the roots of   5 x² - 7 x + 1 = 0

So,  sum of roots = α + β = $\dfrac{-(-7)}{5}$ = $\dfrac{7}{5}$           ...........1

And products of roots = α. β = $\dfrac{1}{5}$                   .................2

Again

The value of $\dfrac{1}{\alpha }$  +  $\dfrac{1}{\beta }$  =  $\dfrac{\alpha +\beta }{\alpha \beta }$

                                  = $\dfrac{\dfrac{7}{5} }{\dfrac{1}{5} }$

                                  = $\dfrac{7\times 5}{1\times 5}$  = 7

So, The value of $\dfrac{1}{\alpha }$  +  $\dfrac{1}{\beta }$  = 7

Hence, The value of $\dfrac{1}{\alpha }$  +  $\dfrac{1}{\beta }$  is 7  Answer