Question

Find alpha ^ - 1 + beta ^ - 1 , if a and are the zeroes of the polynomial a beta 2x ^ 2 - x + 5 .​

Answer 1

Polynomial Given : p(x) = 2x² - x + 5

a = 2 ; b = 1 ; c = 5

$\sf \alpha + \beta = \frac{ - b}{a} = \pink{\bold{\frac{ - 1}{2}}} \\ \\ \sf \: \alpha . \beta = \frac{c}{a} = \pink{\bold{ 5}}$

Now finding α^-1 + β^-1

$\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: { \alpha }^{ - 1} + { \beta }^{ - 1} \: \: \: \: \: \: \: \: \: \: \\ \\ = \frac{1}{ \alpha } + \frac{1}{ \beta } \\ \\ = \frac{ \alpha .\beta }{ \alpha + \beta } \\ \\ \sf= \frac{5}{ \frac{ - 1}{2} } \\ \\ \boxed{\boxed{\green{\bold{ = - 10}}}}$

So the value of α^(-1) + β^(-1) = -10