Question

If Alpha and beta are the zeroes of the polynomial 2x^-4x+5, then find a quadratic polynomial, whose zeroes are 2/Alpha and 2/Beta.​

Answer 1

Answer:

I think 2x^2-4x+5 is not having any zeroes.

It sould be 4x² + 4x +1 

so........

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

MARK BRAINLIEST...

Answer 2

⇒x²-4x+5

⇒α+β = -(-4)/1 = 4

⇒αβ = 5

⇒Have to find a quadratic polynomial, whose zeroes are 2/α and 2/β

Sum of roots = 2/α +2/β = 2(α+β)/αβ = 2(4)/5 = 8/5

Product of roots = 2/α *2/β = 4/αβ = 4/5

⇒Quadratic equation ⇒ x² - (sum of roots) x + Product of roots

⇒So Quadratic equation ⇒  x² - 8x/5 +4/5 = 0

or     5x² - 8x+4 = 0