Question

if alpha and beta are the zeros of the polynomial P(x)= 3x²-12+15 then find the value of beta/alpha +alpha/beta​

Answer 1

Step-by-step explanation:

Given -

α and β are zeroes of polynomial

p(x) = 3x² - 12 + 15

To Find -

Value of β/α + α/β

• » β² + α²/αβ

3x² - 12 + 15

here,

a = 3

b = -12

c = 15

As we know that :-

• α + β = -b/a

» -(-12)/3

» 12/3

• » 4 ........ (i)

And

• αβ = c/a

» 15/3

• » 5 ........ (ii)

Squaring both sides of (i), we get :

(α + β)² = (4)²

» α² + β² + 2αβ = 16

» α² + β² + 2(5) = 16

» α² + β² = 16 - 10

• » α² + β² = 6

Now,

The value of α² + β²/αβ is :

» 6/5

Hence,

The value of α/β + β/α is 6/5

Answer 2

$\huge \mathfrak{Answer:-}$

$\large\underline\mathrm{The \: value \: of \: α² \: + \: β²/αβ \: = \: 6/5}$

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

• α and β are zeroes of the polynomial P(x)= 3x²-12.+15.

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

• Value of β/α + α/β

$\implies$ β² + α²/αβ

$\implies$ 3x²-12+15

$\implies$ a = 3

$\implies$ b = -12

$\implies$ c = 15

$\large\underline\mathrm{Solution}$

$\implies$ α + β = -b/a

$\implies$ -(-12)/3

$\implies$ 4. .....(1)

$\large\underline\mathrm{and}$

$\implies$ (α + β)² = (4)²

$\implies$ α² + β² + 2αβ = 16

$\implies$ α² + β² + 2(5) = 16

$\implies$ α² + β² + 10 = 16

$\implies$ α² + β² = 16 - 10

$\implies$ α² + β² = 6

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

$\large\underline\mathrm{The \: value \: of \: α² \: + \: β²/αβ \: = \: 6/5}$

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