Question

IF
$\alpha \: and \: \beta$
are the zeroes of quadric polynomialf(x)=x^2-5x+4, find the value of
$1 \div \alpha \: + 1 \div \beta - 2 \alpha \beta$
​

Answer 1

Answer:

From the polynomial,

$\alpha + \beta = 5 \\ \alpha \beta = 4 \\ \\ \frac{1}{ \alpha } + \frac{1}{ \beta } - 2 \alpha \beta \\ = \frac{ \alpha + \beta }{ \alpha \beta } - 2 \alpha \beta \\ = \frac{5}{4} - 2 \times 4 \\ = \frac{5 - 32}{4 } \\ = \frac{ - 27}{4}$