Question

If α and β are zeroes of x^2 +7x+7, find the value of 1/α +1/β -2αβ.

Plz help

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Answer 1

the given equation is

x²+7x+7

now...the sum of the zeros is (a-b)=-7

and the product is(ab) =7

now..

$= \frac{1}{a} + \frac{1}{b} - 2ab \\ = \frac{a + b}{ab} - 2ab \\ = \frac{ - 7}{7} - 2 \times 7 \\ = - 1 - 14 \\ = - 15$

Answer 2

Given :-

α and β are zeroes of polynomial x² + 7x + 7

Here, we've to find the value of 1/α +1/β - 2αβ

So first of all, we needa find the zeros if the given polynomial

By quadratic formula, we get

x = [-b ± √(b² - 4ac)]/2a

= (-7 ± √21)/2

➡ x = (-7 + √21)/2 , x = (-7 - √21)/2

➡ α = (-7 + √21)/2 and β = (-7 - √21)/2

Therefore 1/α + 1/β = -1 (refer to the attachment)

2αβ = 2[(-7 + √21)/2 × (-7 - √21)/2]

= 2[(-7 + √21)(-7 - √21)/4]

= 2[(49 - 21)/4]

= 2(28/4)

= 28/2

= 14

Hence, the value of 1/α +1/β - 2αβ :-

= -1 - 14

= -15 Final answer