Question

if alpha and beta are zeros of polynomial x2+2x+1 find the value of 1/alpha+1/beta

Answer 1

Heya

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FOR A GENERAL QUADRATIC EQUATION

ax² + bx + c = 0

Alfa + Beta = - b/a And Alfa × Beta = c/a

=>

Alfa + Beta = -2 And Alfa × Beta = 1

=>

1/Alfa + 1/Beta =

(Alfa + Beta ) / Alfa × Beta

=>

( - 2 ) / 1 = -2

Answer 2

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

Given:

• ${x}^{2} + 2x + 1$

To find:

• Find the value of $\frac{1}{ \alpha } + \frac{1}{ \beta }$

Solution:

Concept to be used:

If $\alpha$ and $\beta$ are zeros of quadratic polynomial $a {x}^{2} + bx + c = 0$ then

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

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

Step 1:

Compare the polynomial with standard polynomial.

On comparison,

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

$\bf \alpha + \beta = - 2...eq1$

$\bf \alpha \beta = 1...eq2$

Step 2:

Calculate the value of $\frac{1}{ \alpha } + \frac{1}{ \beta }$.

Divide eq1 by eq2.

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

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

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

Thus,

The value is $\bf \frac{1}{ \alpha } + \frac{1}{ \beta } = - 2$

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