Question

If α and β are the zeros of the polynomials f(x) = x^2+5x+8 then α×β is………. *

1 point


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Answer 1

Step-by-step explanation:

Given -

α and β are zeroes of polynomial f(x) = x² + 5x + 8

To Find :-

Value of αβ

Method 1 :-

Now,

x² + 5x + 8 = 0

here,

a = 1

b = 5

c = 8

Using Quadratic formula :-

• x = -b ± √b² - 4ac/2a

» -(5) ± √(5)² - 4×1×8/2(1)

» -5 ± √25 - 32/2

» -5 ± √-7/2

Hence,

The zeroes are -

x = -5 + √-7/2

and

x = -5 - √-7/2

And

The value of αβ is

Let α = -5 + √-7/2 and β = -5 - √-7/2

Then,

» -5 + √-7/2 × -5 - √-7/2

» (-5)² - (√-7)²/4

» 25 - (-7)/4

» 25 + 7/4

» 32/4

• » 8

Method 2 :-

αβ = c/a

» 8/1

• » 8

Hence,

The value of αβ is 8

Answer 2

$\huge \mathfrak{Answer:-}$

$\large\underline\mathrm{the \: value \: of \: αβ \: is \: 8.}$

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

• α and β are zeroes of polynomial = x² + 5x + 8.

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

• Value of αβ

$\large\underline\mathrm{Using \: formula}$

$\implies$ x = -b +,- √b² - 4ac/2a

$\implies$ -(5) +,- √(5)² - 4 × 1 × 8/2(1)

$\implies$ -(5) +,- √(5)² - 32/2

$\implies$ -(5) +,- √-7/2

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

$\large\underline\mathrm{The \: zeroes \: are:-}$

$\implies$ -(5) + √-7/2

$\implies$ -(5) - √-7/2

• The value of αβ is

Let α = -(5) + √-7/2 and β = -(5) - √-7/2

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

$\implies$ -(5) + √-7/2 × -(5) - √-7/2

$\implies$ (-5)² - √(-7)²/4

$\implies$ 25 + 7/4

$\implies$ 32/4

$\implies$ 8

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

$\large\underline\mathrm{the \: value \: of \: αβ \: is \: 8.}$

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