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

Explanation:

this is the correct answer for your question

Answer 2

${ \huge{ \underline{ \underline{ \sf{ \green{GivEn : }}}}}}$

• f(x) = 3x² + 8x + 2

${ \huge{ \underline{ \underline{ \sf{ \green{To \: find :}}}}}}$

• Value of α² + β²

• α² - β²

Formula to be used :-

• (a+b)² = a² + b² +2ab

• a² - b² = (a+b)(a-b)

• (a-b)² = a² + b² -2ab

${ \huge{ \underline{ \underline{ \sf{ \green{SoluTion : }}}}}}$

Given,

a polynomial __ 3x² + 8x + 2

Where,

a = 3

b = 8

c = 2

Sum of zeroes

= α + β

= -b/a

= -8/3

Product of zeroes

= αβ

= c/a

= 2/3

___________________________________________________

Now, find the value of α² + β²

⟶ (α + β)² = α² + β² + 2αβ

⟶ (α + β)² - 2αβ = α² + β²

⟶ α² + β² = (-8/3)² -2×2/3

⟶ α² + β² = 64/9 -4/3

⟶ α² + β² = 52/9

_________________________________________________

Again, find the value of α² - β²

⟶ (a-b)² = a² + b² -2ab

⟶ (a-b) = √a² + b² -2ab

⟶ 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 ×2√10/3

⟶ α² - β² = -16√10/9

_________________________________________________

Hence, value of α² + β² = 52/9

and α² - β² = -16√10/9.