Question

. If α and β are zeroes of x2 – 4x + 1, then 1/α + 1/β – αβ is​

Answer 1

Answer:

x

2

−4x+1

Comparing to the general quadratic equation,

ax^2+bx+cax

2

+bx+c

Where,

a= 1, b= -4, c= 1

Given that α and β are zeroes of the polynomial.

From the properties of the zeros,

\begin{lgathered}\alpha +\beta =-\dfrac{b}{a}=\dfrac{4}{1}=4\\\\ \alpha \cdot \beta=\dfrac{c}{a}=\dfrac{1}{1}=1\end{lgathered}

α+β=−

a

b

=

1

4

=4

α⋅β=

a

c

=

1

1

=1

Then,

=\dfrac{1}{\alpha}+\dfrac{1}{\beta}-\alpha\beta=

α

1

+

β

1

−αβ

=\dfrac{\alpha+\beta}{\alpha\beta}-\alpha\beta=

αβ

α+β

−αβ

=\dfrac{4}{1}-1=

1

4

−1

=4-1=4−1

=3=3