Question

If α and β are the zeroes of the polynomial f(x) = 4x^2

– 6x + 2, then the value of α^2

– β^

2

is​

Answer 1

Answer:

-3÷4 or 3/4

Step-by-step explanation:

factorise and find two zero then put

Answer 2

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• Zeroes of the given polynomial are α and β

• A polynomial f(x) = 4x² - 6x + 2

Where,

a = 4

b = -6

c = 2

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

•The value of α² - β²

Formula to be used :-

• (a - b)² = a² + b² - 2ab

• a -b = √a² + b² - 2ab

• (a + b)² = a² + b² + 2ab

• a² + b² = (a + b)² - 2ab

• (a + b)(a - b) = a² - b²

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

We know,

Sum of zeroes = -b/a

Product of zeroes = c/a

Now, find s um of zeroes of the given polynomial.

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Sum of zeroes = -b/a

⟶ α + β = -(-6)/4

⟶ α + β = 6/4

⟶ α + β = 3/2

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Again,

Product of zeroes = c/a

⟶ αβ = 2/4

⟶ αβ = 1/2

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Now,

α² + β² = (α + β )² - 2αβ

= (3/2)² - 2 × 1/2

= 9/4 -1

= (-4+9)/4

= 5/4...........eq(1)

Hence,

α² - β²

= (α + β)(α - β)

= (α + β) (√α² + β² - 2αβ)

Substitute the acquired values

= (3/2) (√5/4 - 2 × ½)

= (3/2) (√5/4 -1)

= (3/2) (√(5 -4)/4)

= 3/2 × 1/2

= 3/4

Therefore, value of α² - β² = 3/4

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