Question

If alfa and bita are the zeroes of polynomials x²-3x+2 then find alfa²+bita²,bita²+alfa

Answer 1

Step-by-step explanation:

Correct Question :-

• If α and β are zeroes of polynomial x² - 3x + 2 Then, Find the value of α² + β²

Given -

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

To Find -

• Value of α² + β²

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 α² + β² is

→ (2)² + (1)²

→ 5

Hence,

The value of α² + β² is 5

Method 2 :-

As we know that :-

• αβ = c/a

→ αβ = 2/1

And

• α + β = -b/a

→ α + β = -(-3)/1

→ α + β = 3

Squaring both sides :-

→ (α + β)² = (3)²

→ α² + β² + 2αβ = 9

→ α² + β² = 9 - 2(2)

→ α² + β² = 9 - 4

→ α² + β² = 5

Hence,

The value of α² + β² is 5

Answer 2

$\large{\underline{\bf{\purple{Correct\:Question:-}}}}$

if α and β are the zeroes of the polynomial

x² - 3x +2 then find the value of α² + β².

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$\large{\underline{\bf{\green{Given:-}}}}$

• ✰ p(x) = x² - 3x +2

$\large{\underline{\bf{\green{To\:Find:-}}}}$

• ✰ we need to find the value of α² + β².

$\huge{\underline{\bf{\red{Solution:-}}}}$

p(x) = x² - 3x +2

$\mapsto \rm\:x^2 -x - 2x+2$

$\mapsto \rm\:x(x-1)-2(x-1)$

$\mapsto \rm\:(x -2)(x-1)$

$\mapsto \rm\:x=2 \:or\:x=1$

• Let α = 2
• and β = 1

Now ,

finding value of α² + β²

α² + β² = (2)² + (1)²

α² + β² = 4 + 1

α² + β² = 5

So,

Value of α² + β² = 5.

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