Question

If alpha , beta are the zeros of polynomial x2+x+1 then 1/alpha +1/beta=?

Answer 1

Solution : By taking L.C.M of dinominators

→ 1/α + 1/β = (α + β)/αβ

Since we know that,

→ α + β = - Coefficient of x/Coefficient of x²

→ α + β = - 1/1 = - 1

→ αβ = Constant Term/Coefficient of x²

→ αβ = 1/1 = 1

∴ (α + β)/αβ = - 1/1

→ - 1

Answer : - 1

Answer 2

Answer:

-1

Step-by-step explanation:

We are given that a polynomial

$x^2+x+1$

Two zeroes of polynomial are $\alpha,\beta$.

We have to find the value of

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

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

General quadratic polynomial

$x^2-(\alpha+\beta)x+\alpha\cdot \beta$

Compare with given equation

$\alpha+\beta=-1$

$\alpha\cdot \beta=1$

Substitute the values then we get

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

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