Question

if alpha and beta are the zeroes of the polynomial x2+6x+2 then the balue of 1/alpha +1/beta is
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Answer 1

Given,

• α and β are the roots of the equation x² +6x +2 = 0

Here,

• coefficient of x² (a) = 1

• coefficient of x (b) = 6

• coefficient of c (c) = 2

We know,

• $\sf{\alpha+\beta=\dfrac{-b}{a}}$

• $\sf{\alpha\beta=\dfrac{c}{a}}$

Applying the values to the equation,

$\implies \sf{\alpha+\beta=\dfrac{-6}{1} \ \ \ \ \& \ \ \ \ \alpha\beta=\dfrac{2}{1}}$

$\implies \sf{\alpha+\beta=-6 \ \ \ \ \& \ \ \ \ \alpha\beta=2}$

Now,

• We have to find   $\sf{\dfrac{1}{\alpha}+\dfrac{1}{\beta}}$.

$\implies \sf{\dfrac{1}{\alpha}+\dfrac{1}{\beta}=\dfrac{\alpha+\beta}{\alpha\beta}}$

$\implies \sf{\dfrac{1}{\alpha}+\dfrac{1}{\beta}=\dfrac{-6}{2}}$

$\implies \sf{\dfrac{1}{\alpha}+\dfrac{1}{\beta}=-3}$

$\boxed{\bold{\sf{\therefore \dfrac{1}{\alpha}+\dfrac{1}{\beta}=-3}}}$