Question

if alpha and beta are the zeros of the quadratic polynomial f x is equal to x square - 2 x minus 8 then find the value of Alpha square minus beta square​

Answer 1

Step-by-step explanation:

α + ß = -(b/a) = -(-2) = 2

αß = (c/a) = (-8)

we have to find : α²- ß²

Ans:

α²- ß² = (α+ß)²- 2αß

= (2)² - 2×(-8)

= 4 - (-16)

=20

Answer 2

GivEn:

• $\sf \alpha\;and\;\beta$ are the zeros of the quadratic polynomial f(x) = $\sf x^2 - 2x - 8$.

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To find:

• Value of $\sf \alpha^2 - \beta^2$.

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SoluTion:

GivEn that,

$\sf \star\; f(x) = x^2 - 2x - 8$

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where,

• a = 1
• b = -2
• c = -8

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Therefore,

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★ Sum of zeros, $\sf ( \alpha + \beta ) = \dfrac{-b}{a}$

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$:\implies\sf - \dfrac{-2}{1} = \bf{2}$

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★ Product of zeros, $\sf ( \alpha \beta ) = \dfrac{c}{a}$

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$:\implies\sf \dfrac{-8}{1} = \bf{-8}$

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Therefore,

★ Value of $\sf \alpha^2 - \beta^2$ is,

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$:\implies\sf ( \alpha + \beta )^2 - 2 \alpha \beta\;\;\;\;\;\;\;\bigg\lgroup\bf ( \alpha + \beta )^2 = { \alpha}^2 + { \beta}^2 + 2 \alpha \beta \bigg\rgroup$

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$\;\;\;\;\;\;\small\sf \underline{Putting\;values\;:}$

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$:\implies\sf (2)^2 - 2 \times -8$

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$:\implies\sf 4 + 16$

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$:\implies{\underline{\boxed{\bf{\pink{20}}}}}\;\bigstar$

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$\therefore$ Hence, The value of $\sf \alpha^2 - \beta^2$ is 20.