Question

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

Answer 1

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Answer 2

Answer-

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

Solution-

The given quadratic equation,

$x^2-4x+1$

Comparing to the general quadratic equation,

$ax^2+bx+c$

Where,

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

Given that α and β are zeroes of the polynomial.

From the properties of the zeros,

$\alpha +\beta =-\dfrac{b}{a}=\dfrac{4}{1}=4\\\\ \alpha \cdot \beta=\dfrac{c}{a}=\dfrac{1}{1}=1$

Then,

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

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

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

$=4-1$

$=3$