Question

if alpha and beta are zeros of a quadratic polynomial 4 x square + 4 x + 1 then form a quadratic polynomial whose zeros are 2 alpha and 2 Beta

Answer 1

α and β are the zeroes of 4x² + 4x +1 
a = 4 
b  =4 
c = 1
sum of zeroes = -b/a
α + β = -b/a
α+ β = -4 /4 
α + β = -1 ........................(i)

product of zeroes  = c/a
αβ = c/a
αβ = 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

Answer 2

Answer:

Step-by-step explanation:α and β are the zeroes of 4x² + 4x +1 

a = 4 

b  =4 

c = 1

sum of zeroes = -b/a

α + β = -b/a

α+ β = -4 /4 

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

product of zeroes  = c/a

αβ = c/a

αβ = 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