Question

if alpha and beta are the zeros of the polynomial f x is equal to X square + X + 1 find one by Alpha Plus One by beta​

Answer 1

Given :

alpha and beta are the zeroes of the polynomial

$f(x) = x {}^{2} + x + 1$

To find :

Value of

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

$\huge{\mathcal{\blue{\underline{Answer}}}}$

Sum of the zeroes :

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

Where

b=1

a=1

Product of the zeroes :

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

Now solving :

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

Putting the values we get

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

$\huge{\mathcal{\blue{\underline{1/a+1/b=-1}}}}$