Question

in the alpha and beta are zeros of x^2+7+7, find the value of 1/alpha+1/beta+alpha ×beta?​

Answer 1

Answer:

The value of

α

1

+

β

1

−2αβ is −15

Step-by-step explanation:

Given that α and β are the zeroes of the polynomial

x^2+7x+7x

2

+7x+7

we have to find the value of

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

α

1

+

β

1

−2αβ

The polynomial is x^2+7x+7x

2

+7x+7

By comparing with standard form ax^2+bx+c=0ax

2

+bx+c=0

⇒ a=1, b=7 and c=7

\text{Sum of zeroes= }\alpha+\beta=\frac{-b}{a}=-\frac{-7}{1}=-7Sum of zeroes= α+β=

a

−b

=−

1

−7

=−7

\text{Product of zeroes= }\alpha.\beta=\frac{c}{a}=\frac{7}{1}=7Product of zeroes= α.β=

a

c

=

1

7

=7

Now,

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

α

1

+

β

1

−2αβ

=\frac{\beta+\alpha}{\alpha \beta}-2\alpha \beta=

αβ

β+α

−2αβ

=\frac{-7}{7}-2(7)=-1-14=-15=

7

−7

−2(7)=−1−14=−15