Question

if alpha and beta are the roots of equation 9 X square + 6 X + 1 equal to zero write the value of one by Alpha Plus One by beta

Answer 1

Hi friend
---------------
Your answer
-----------------------

Equation => 9x² + 6x + 1

Factorising the equation , we get ,

9x² + 6x + 1

=> 9x² + 3x + 3x + 1

=> 3x(3x + 1) + 1(3x + 1)

=> (3x + 1)(3x + 1)

Now,
---------

zeroes of the equation , are

3x + 1 = 0

=> 3x = - 1

=> x = - 1/3

As , the factors are same (3x + 1) , that means the zeroes are same .

Let alpha = -1/3 and beta = -1/3

Then,
----------

Alpha + 1/beta


$\alpha + \frac{1}{ \beta } \\ \\ = > \frac{ - 1}{3} + \frac{1}{ \frac{ - 1}{3} } \\ \\ = > \frac{ - 1}{3} - 3 \\ \\ = > \frac{ - 1 - 9}{3} \\ \\ = > \frac{ - 10}{3}$
HOPE IT HELPS