Question

if alpha and beta are zeros of polynomial P of x is equal to X square + X - 1 then find the value of one upon alpha plus one upon beta​

Answer 1

Answer:

1

Step-by-step explanation:

α and β are roots of the equation

p(x) = x² + x - 1

a = 1, b = 1 c = -1

Sum of roots, α + β = -b/a = -1/1 = -1

product of roots = c/a = -1/1 = -1

Now,

1/α + 1/β = α + β / αβ = -1 / -1  = 1.

Answer 2

The required result is 1

Step-by-step explanation:

Given: α and β are the zeroes  of the quadratic polynomial $x^2+x-1$

To find: $\dfrac{1}{\alpha}+ \dfrac{1}{\beta}$

Therefore

As we know the standard quadratic polynomial is of the form

$ax^2+bx+c$

By comparing we get

a= 1, b=1 , c= -1

Now as we know

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

$\alpha\beta= \dfrac{c}{a} =\dfrac{-1}{1} =-1$

Now

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

Hence , the required result is 1

#Learn  more

If alpha , beta are the zeros of polynomial x2+x+1 then find $\dfrac{1}{\alpha}+ \dfrac{1}{\beta}$

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