Question

Q6lf
$\alpha$
and
$\beta$
are thee zeroes of the quadratic polynomial x
${x}^{2}$
+ x + 1.
Then
$\frac{1}{ \alpha } + \frac{1}{ \beta } =$

​

Answer 1

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

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

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

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

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

NOTE THAT:

$a = cofficient \: of \: {x}^{2}$

b = cofficient of {x}

c = constant term

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