Question

If alpha, beta are the zeros of the polynomial f(x) = x2 – 3x + 2, then find 1/ alpha + 1/beta.
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Answer 1

Answer:

3/2

Step-by-step explanation:

Quadratic polynomials in form of x² - Sx + P represent S as the sum of roots and P as the product of the roots.

Compare x² - 3x + 2 with x² - Sx + P

If α and β are roots:

S = α + β = 3     ;   P = αβ = 2

 Therefore,

⇒ 1/α + 1/β

⇒ (β + α)/αβ

⇒ (α + β)/αβ

⇒ 3/2             [from above]

Answer 2

Required Answer :-

At first we need to find sum of zeroes

$\sf Sum = \alpha +\beta$

Sum = 3

Now

$\sf Product = \alpha \beta$

Product = 2 $\times$ 1

Product = 2

Now

1/α + 1/β

• $\sf Taking \: \alpha \; and \;\beta \; as \; common$

(β + α)/αβ

Now

$\sf \dfrac{(\alpha +\beta )}{\alpha \beta }$

Since,

$\alpha +\beta =3$

and

$\alpha \beta =2$

3/2