Answer:
a) -27/4
Step-by-step explanation:
f(x) =x² - 5x + 4
a= 1; b = -5 and c = 4
We can find the sum of zeros and product of zeroes by the formula.
[tex]\sf \alpha + \beta = \dfrac{-b}{a}\\\\\\~~~~~~~~~ = \dfrac{-(-5)}{1}\\\\\\~~~~~~~~ ~ = 5[/tex]
[tex]\sf \alpha \beta = \dfrac{c}{a}\\\\\\~~~~~~ = \dfrac{4}{1}\\\\\\~~~~~~ = 4[/tex]
[tex]\sf \dfrac{1}{\alpha }+ \dfrac{1}{\beta }-2\alpha \beta = \dfrac{1*\beta }{\alpha *\beta }+ \dfrac{1*\alpha }{\beta *\alpha }-2\alpha \beta[/tex]
[tex]\sf = \dfrac{\alpha +\beta }{\alpha \beta }-2\alpha \beta \\\\\\Now \ substitutte \ the \ values \ (\alpha + \beta) \ and \ \alpha \beta,\\\\\\= \dfrac{5}{4}-2*4\\\\\\= \dfrac{5}{4}- \dfrac{8*4}{1*4}\\\\= \dfrac{5}{4}- \dfrac{32}{4}\\\\= \dfrac{-27}{4}[/tex]
