If α, β are zeroes of x2+7x+7, find the value of 1/α + 1/β - 2 α�

1.	If α, β are zeroes of x2+7x+7, find the value of 1/α + 1/β - 2 αβ.
Answer» ANSWER: The value of above expression = (-15) GIVEN: α, β are ZEROES of x²+7x+7. TO FIND: $\frac{1}{ \alpha} + \frac{1}{ \beta} - 2 \alpha \beta$ SOLUTION p(X) = x²+7x+7 $\implies \: \alpha + \beta = \frac{ - (coefficient \: of \: x)}{coefficient \: of \: x {}^{2} } \\ \implies \: \alpha + \beta = \frac{ - 7}{1} \\ \\ \implies \: \alpha \beta = \frac{(constant \: term)}{coefficient \: of \: x {}^{2} } \\ \implies \alpha \beta \: = \frac{7}{1}$ Now putting the VALUES in the above expression. $= (\frac{1}{ \alpha} + \frac{1}{ \beta}) - 2 \alpha \beta \\ = ( \frac{\alpha + \beta}{\alpha \beta} ) - 2\alpha \beta \\ = ( \frac{ - 7}{7} ) - (2 \times 7) \\ = - 1 - 14 \\ = - 15$ So the value of above expression = (-15) NOTE: *some* *IMPORTANT* *formulas* $\implies \: \alpha + \beta = \frac{ - (coefficient \: of \: x)}{coefficient \: of \: x {}^{2} } \\ \\ \implies \: \alpha \beta = \frac{(constant \: term)}{coefficient \: of \: x {}^{2} }$

If α, β are zeroes of x2+7x+7, find the value of 1/α + 1/β - 2 αβ.

Answer»

ANSWER:

The value of above expression = (-15)

GIVEN:

α, β are ZEROES of x²+7x+7.

TO FIND:

$\frac{1}{ \alpha} + \frac{1}{ \beta} - 2 \alpha \beta$

SOLUTION

p(X) = x²+7x+7

$\implies \: \alpha + \beta = \frac{ - (coefficient \: of \: x)}{coefficient \: of \: x {}^{2} } \\ \implies \: \alpha + \beta = \frac{ - 7}{1} \\ \\ \implies \: \alpha \beta = \frac{(constant \: term)}{coefficient \: of \: x {}^{2} } \\ \implies \alpha \beta \: = \frac{7}{1}$

Now putting the VALUES in the above expression.

$= (\frac{1}{ \alpha} + \frac{1}{ \beta}) - 2 \alpha \beta \\ = ( \frac{\alpha + \beta}{\alpha \beta} ) - 2\alpha \beta \\ = ( \frac{ - 7}{7} ) - (2 \times 7) \\ = - 1 - 14 \\ = - 15$

So the value of above expression = (-15)

NOTE:

some IMPORTANT formulas

$\implies \: \alpha + \beta = \frac{ - (coefficient \: of \: x)}{coefficient \: of \: x {}^{2} } \\ \\ \implies \: \alpha \beta = \frac{(constant \: term)}{coefficient \: of \: x {}^{2} }$