Question

If alpha and beta are the zeroes of x2 - 5x + 4 ,then find the value of 1/alpha + 1/beta-2alphabeta

Answer 1

Hey user here is your answer..

see the attachment

Answer 2

Answer:

$\text{The value is }\frac{-27}{4}$

Step-by-step explanation:

Given that α and β are the zeroes of the polynomial

$x^2-5x+4$

we have to find the value of

$\frac{1}{\alpha}+\frac{1}{\beta}-2\alpha \beta$

$x^2-5x+4$

By comparing with standard form $ax^2+bx+c=0$

⇒ a=1, b=5 and c=4

$\text{Sum of zeroes= }\alpha+\beta=\frac{-b}{a}=-\frac{-5}{1}=5$

$\text{Product of zeroes= }\alpha.\beta=\frac{c}{a}=\frac{4}{1}=4$

Now,

$\frac{1}{\alpha}+\frac{1}{\beta}-2\alpha \beta$

$=\frac{\beta+\alpha}{\alpha \beta}-2\alpha \beta$

$=\frac{5}{4}-2(4)=\frac{5}{4}-8=\frac{-27}{4}$