Question

if alpha and beta are the zeroes of the
polynomial x2+4x+6 then the value of
1/alpha+1/beta lies between​

Answer 1

Answer:

The value of  $\frac{1}{\alpha } +\frac{1}{\beta }$  =  $\frac{-2}{3}$

Step-by-step explanation:

Given,

α and β are zeroes of the polynomial x²+4x+6

To find

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

Recall the concept,

If α and β are zeroes of the polynomial ax²+bx+c,

Then sum of roots = α+ β = $\frac{-b}{a}$ and α× β = $\frac{c}{a}$

Solution:

Given that α and β are zeroes of the polynomial x²+4x+6

Then we have α+ β = -4 and α× β = 6

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

Substituting the value of α+ β and  α× β

$\frac{1}{\alpha } +\frac{1}{\beta }$ = $\frac{\alpha +\beta }{\alpha \beta }$  = $\frac{-4}{6}$ = $\frac{-2}{3}$

∴ $\frac{1}{\alpha } +\frac{1}{\beta }$ = $\frac{-2}{3}$

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Answer 2

Answer:

$\frac{1}{\alpha } + \frac{1}{\beta } = \frac{-2}{3}$

Step-by-step explanation:

zeroes of the polynomial x²+4x+6 are α and β

on comparing with ax²+bx+c

a = 1 ,b= 4 ,c =6

sum of roots of polynomial = α +β  = -b/a = -4/1

product of roots of polynomial = α * β = c/a  = 6/1

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

$\frac{1}{\alpha } + \frac{1}{\beta } = \frac{-4}{6}$

$\frac{1}{\alpha } + \frac{1}{\beta } = \frac{-2}{3}$ (ans)

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