Question

if alpha and beta are zeroes of x²- 2x +1 then find 1/alpha+ 1/beta​

Answer 1

Answer:

1/α + 1/β = 2

Step-by-step explanation:

x² - 2x + 1

α+β = -b/a

= - (-2) /1

= 2

αβ = c/a

1/1

= 1

now,

1/α + 1/β

Taking LCM:

α + β / αβ

Subtituting values of α + β and αβ

= 2 /1

= 2

I HOPE THIS WILL HELP YOU OUT :)

Answer 2

Question:

if $\alpha$ and $\beta$ are zeroes of $x^2- 2x +1$ then find $\frac{1}{\alpha} + \frac{1}{\beta}$

Answer:

We have to find $\frac{1}{\alpha} + \frac{1}{\beta}$

$\frac{1}{\alpha} + \frac{1}{\beta}\implies \frac{\alpha + \beta}{ \alpha \beta} - - - [i]$

Find $\alpha+ \beta$ and $\alpha \beta$ separately.

For equation $f(x) = x^2- 2x +1$,

$\alpha+ \beta= \frac{-b} {a} \implies \frac{-(-2)}{1} \implies 2$

$\alpha \beta = \frac{c} {a} \implies \frac{1}{1} \implies 1$

Putting the values in [i], we have:

$\frac{\alpha + \beta}{ \alpha \beta} =\frac{2}{1} \implies 2$

Hence, 2 is the answer.