Question

If alfa and beta are zeroes of a quadratic polynomial x2-4x+3, then from a quadratic polynomial whose zeroes are 1 / alfa and 1/ beta ..

Answer 1

Hi friend!!

Given,alfa and beta are zeroes of a quadratic polynomial x2-4x+3

→œ+ß=-b/a=4

→œß=c/a=3

Given, 1/œ,1/ß are the zeros

→1/œ+1/ß=(œ+ß)/œß=4/3

→1/œß=1/3


so, the quadratic polynomial would be
x²-4x/3+1/3


I hope this will help u ;)

Answer 2

Hi there !!

p(x) = x² - 4x + 3

a = 1

b = -4

c = 3


α and β are the zeros of p(x)

We know that sum of zeros = -b/a

that is ,
α + β = -b/a = -(-4)/1 = 4

α + β =  4
Also ,

Product of zeros = c/a = 3
αβ = 3

To find :-
Given , 

1/α and 1/β are zeroes of a polynomial

Sum of zeros = $\frac{1}{ \alpha } + \frac{1}{ \beta }$

$\frac{1}{ \alpha } + \frac{1}{ \beta }$ =  $\frac{ \alpha + \beta }{ \alpha \beta }$
                        = $\frac{4}{3}$


Product of zeros = 1/α × 1/β = 1/αβ  = 1/3

A quadratic polynomial can be formed :-

x² - (sum of zeros)x + (product of zeros)
 

x² - (4/3)x + 1/3
 = x²-4x/3+1/3               ----> Required polynomial