Question

if alpha and beta are zeroes of quadratic ploynomial 4x²+4x+1 then form a quadratic polynomial whose zeroes 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

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Answer 2

Hello sir/ma'am your answer is here :

F(x) = 4xsq.+4x+1

Zeros =α&β

α+β= —b/a

αβ= c/a

= 1 & 1/4

Now, 2α,2β

2α+2β = 2(α+β) = 2×1 = 2

2α×2β = 4(1/4) = 4/4 = 1

So, equation is X sq. —2x + 1

Answer