Question

if alpha , beta are the zeros of the polynomial f(X)= X square + x+ 1, then one upon alpha plus one upon beta is equal to

Answer 1

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Answer 2

Answer:

$\frac{1}{\alpha}+\frac{1}{\beta}=-1$

Step-by-step explanation:

Given : If alpha,beta are the zeros of the polynomial f(x)= x² + x+ 1.

To find : One upon alpha plus one upon beta is equal to?

Solution :

The zeros of the polynomial $f(x)=ax^2+bx+c$

are $\alpha +\beta=-\frac{b}{a}$ and $\alpha\times \beta=\frac{c}{a}$

Comparing with $f(x)=x^2+x+1$ the equation form is

$\alpha +\beta=-\frac{b}{a}$

$\alpha +\beta=-\frac{1}{1}$

$\alpha +\beta=-1$......(1)

and $\alpha\times \beta=\frac{c}{a}$

$\alpha\times \beta=\frac{1}{1}$

$\alpha\times \beta=1$ .....(2)

Now, we have to find $\frac{1}{\alpha}+\frac{1}{\beta}$

Solve the equation,

$=\frac{\beta+\alpha}{\alpha\times \beta}$

Substitute the value from eqn (1) and (2),

$=\frac{-1}{1}$

$=-1$

Therefore, $\frac{1}{\alpha}+\frac{1}{\beta}=-1$