Question

if alpha. bitaa are the zero of the polynomial f (x) x2-3x+2 than find 1/alpha+1/ bitaa ​

Answer 1

Step-by-step explanation:

Given -

• α and β are zeroes of the polynomial f(x) = x² - 3x + 2

To Find -

• Value of 1/α + 1/β

→ β + α/αβ

Method 1 :-

Now,

→ x² - 3x + 2

By middle term splitt :-

→ x² - x - 2x + 2

→ x(x - 1) - 2(x - 1)

→ (x - 2)(x - 1)

Zeroes are -

→ x - 2 = 0 and x - 1 = 0

→ x = 2 and x = 1

Then,

The value of 1/α + 1/β is

→ 1/1 + 1/2

→ 2 + 1/2

→ 3/2

Hence,

The value of 1/α + 1/β is 3/2

Method 2 :-

As we know that :-

• α + β = -b/a

→ α + β = -(-3)/1

→ α + β = 3

And

• αβ = c/a

→ αβ = 2/1

→ αβ = 2

Then,

The value of 1/α + 1/β or α + β/αβ is

→ 3/2

Answer 2

$\large{\boxed{\underline{\underline{\bf{\red{Answer:-}}}}}}$

$\implies$ x = 2

$\implies$ x = 1

$\large\underline\mathrm{Given:-}$

• β and α x² - 3x + 2 are zeroes of the polynomial f(x) = x² - 3x + 2

$\large\underline\mathrm{To \: find}$

• Value of 1/α + 1/β

$\implies$ β + α/βα

$\large\underline\mathrm{Now,}$

$\implies$ x² - 3x + 2

$\implies$ x² - x - 2x + 2

$\implies$ x(x - 1) - 2(x - 1)

$\implies$ (x - 2)(x - 1)

$\implies$ x - 2 = 0

$\implies$ x = 2

$\implies$ x - 1 = 0

$\implies$ x = 1

$\large\underline\mathrm{Then,}$

$\large\underline\mathrm{The \: value of \: 1/α \: + 1/β \: is \: 3/2 \: .}$

$\implies$ α + β = -b/a

$\implies$ α + β = -(-3)/1

$\implies$ α + β = 3

$\large\underline\mathrm{And}$

$\implies$ βα = c/a

$\implies$ βα = 2/1

$\implies$ βα = 2

$\large\underline\mathrm{Then,}$

$\large\underline\mathrm{The \: value of \: 1/α + \: 1/β \: or \: α \: + \: β/βα \: is \: 3/2 \: .}$

$\large\underline\mathrm{Hope \: it \: helps \: you \: plz \: mark \: me \: brainlist}$