Question

if alpha and beta are the zeroes of the polynomial 3x2 +8x +2 find the value of (i) alpha 2 + beta 2 (ii) alpha2 - beta 2

Answer 1

Answer:

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Answer 2

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

• p(x) = 3x² + 8x + 2

$\large\bf\underline {To \: find:-}$

• Value of α² + β²
• α² - β²

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

• p(x) = 3x² + 8x + 2

➝ α + β = -b/a

➝ α + β = -8/3

➝ αβ = c/a

➝ αβ = 2/3

we know that

• (a+b)² = a² + b² +2ab

➝(α + β)² = α² + β² + 2αβ

➝ (α + β)² - 2αβ = α² + β²

Value of α² + β² :-

➝ α² + β² = (-8/3)² -2×2/3

➝ α² + β² = 64/9 -4/3

➝ α² + β² = (64 -12)/9

➝ α² + β² = 52/9

we know that :-

• a² - b² = (a+b)(a-b)

➝ α² - β² = (α+β)(α-β)

and

➝ (a-b)² = a² + b² -2ab

➝ (a-b) = √a² + b² -2ab

Value of α² - β²

➝ α² - β² = (a+b)(√a² + b² -2ab)

➝ α² - β² = -8/3(√(52/9-2×2/3)

➝ α² - β² = -8/3(√(52-12)/9

➝ α² - β² = -8/3 (√40/9)

➝ α² - β² = -8/3 ×2√10/3

➝α² - β² = -16√10/9

So,

Value of α² + β² = 52/9 and α² - β² = -16√10/9.