Question

if alpha beta are the zeros of the polynomial x square + x + 1 then find the value of one upon alpha + 1 upon beta
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Answer 1

Given :-

• Quadratic equation : x² + x + 1.

To Find :-

• The value of $\large\frac{1}{ \alpha } + \frac{1}{ \beta }$.

Solution :-

Given that, x² + x + 1 .

On comparing with ax² + bx + c : We get,

↪a = 1 , b = 1 , c = 1

Given that, α & β are the zeroes of the quadratic polynomial.

↪Sum of roots = -b/a

↪α + β = -1/1

↪α + β = -1

↪ Product of zeroes = c/a

↪αβ = 1/1

↪αβ = 1

Now,

↪1/α + 1/β = α + β/αβ

↪1/α + 1/β = -1/1

↪1/α + 1/β = -1

Hence,

• The value of $\large\frac{1}{ \alpha } + \frac{1}{ \beta }$ is -1.

Answer 2

Answer:

Given :-

Quadratic equation : x² + x + 1.

To Find :-

The value of \large\frac{1}{ \alpha } + \frac{1}{ \beta }

α

1

+

β

1

.

Solution :-

Given that, x² + x + 1 .

On comparing with ax² + bx + c : We get,

↪a = 1 , b = 1 , c = 1

Given that, α & β are the zeroes of the quadratic polynomial.

↪Sum of roots = -b/a

↪α + β = -1/1

↪α + β = -1

↪ Product of zeroes = c/a

↪αβ = 1/1

↪αβ = 1

Now,

↪1/α + 1/β = α + β/αβ

↪1/α + 1/β = -1/1

↪1/α + 1/β = -1

Hence,

The value of \large\frac{1}{ \alpha } + \frac{1}{ \beta }

α1 +

β1is -1.