Question

Quadratic polynomial 2xsquare-4x+5 than find the sum of zeroes and the product of zeroes

Answer 1

Α and β are the zeroes of 4x² + 4x +1 

a = 4 

b  =4 

c = 1
sum of zeroes =
$- \frac{b}{a}$

α + β =
$- \frac{b}{a}$

α+ β =
$- \frac{4}{4}$

α + β = -1 ........................(i)

product of zeroes  =
$\frac{c}{a}$

αβ =
$\frac{c}{a}$

αβ =
$\frac{1}{4}$
...............(ii)


zeroes of polynomial are 2α and 2β

so 

sum of zeroes = 

2α + 2 β

2(α+β)         from (i)

2(-1)

-2


product of zeroes 

(2α)(2β)

4αβ

4 (1/4)                  from (ii)

1 


polynomial = 

x ² - ( sum of zeroes )x + product of zeroes

x² - (-2)x +1

x² +2 x+1

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