Question

if alpha and betta are the zeroes of 2x^2-9x+10, form the polynomial whose zeroes are 1/alpha and 1/betta​

Answer 1

Answer:

10x² - 9x + 2 .l

Step-by-step explanation:

Given:

Alpha and betta are the zeroes of 2x²-9x+10,

To form:

Polynomial whose zeroes are 1/alpha and 1/beta

Solution:

First we should know the value of alpha and beta .

$2 {x}^{2} - 9x + 10 = 0 \\ \\ 2 {x}^{2} - 5x - 4x + 10 = 0 \\ \\ x(2x - 5) - 2(2x - 5) = 0 \\ \\ (x - 2)(2x - 5)$

Either, x - 2 = 0

x = 2

or, 2x - 5 = 0

or, 2x = 5

or, x = 5/2

So, Alpha = 5/2 or 2

Beta = 2 or 5/2

Hence, 1/Alpha = 2/5 or 1/2

1/Beta = 1/2 or 2/5

Therefore the polynomial whose zero is 1/alpha and 1/beta is ......

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

x² - (2/5 + 1/2)x + (2/5×1/2)

x² - (4+5)/10x + 1/5

x² - 9x/10 +1/5

And in balanced form,

10x² - 9x + 2

The required polynomial is 10x² - 9x + 2 .

Answer 2

Answer:

Given that,

Given that,α and β are Zeroes, then equation will be

Given that,α and β are Zeroes, then equation will bex2−(α+β)+αβ=0

Given that,α and β are Zeroes, then equation will bex2−(α+β)+αβ=0Given equation is 4x2+4x+1=0 

Given that,α and β are Zeroes, then equation will bex2−(α+β)+αβ=0Given equation is 4x2+4x+1=0 ∴α+β=4−4=−1αβ=41

Given that,α and β are Zeroes, then equation will bex2−(α+β)+αβ=0Given equation is 4x2+4x+1=0 ∴α+β=4−4=−1αβ=41Now, new zeroes are 2α and 2β

Given that,α and β are Zeroes, then equation will bex2−(α+β)+αβ=0Given equation is 4x2+4x+1=0 ∴α+β=4−4=−1αβ=41Now, new zeroes are 2α and 2βthen,

Given that,α and β are Zeroes, then equation will bex2−(α+β)+αβ=0Given equation is 4x2+4x+1=0 ∴α+β=4−4=−1αβ=41Now, new zeroes are 2α and 2βthen,2α+2β=2(α+β)=2(−1)=−22α×2β=2αβ=4×(41)=1

Given that,α and β are Zeroes, then equation will bex2−(α+β)+αβ=0Given equation is 4x2+4x+1=0 ∴α+β=4−4=−1αβ=41Now, new zeroes are 2α and 2βthen,2α+2β=2(α+β)=2(−1)=−22α×2β=2αβ=4×(41)=1So the quadratic  polynomial will be

Given that,α and β are Zeroes, then equation will bex2−(α+β)+αβ=0Given equation is 4x2+4x+1=0 ∴α+β=4−4=−1αβ=41Now, new zeroes are 2α and 2βthen,2α+2β=2(α+β)=2(−1)=−22α×2β=2αβ=4×(41)=1So the quadratic  polynomial will bex2−(−2)x−1=0⇒x2+2x+1=0

Given that,α and β are Zeroes, then equation will bex2−(α+β)+αβ=0Given equation is 4x2+4x+1=0 ∴α+β=4−4=−1αβ=41Now, new zeroes are 2α and 2βthen,2α+2β=2(α+β)=2(−1)=−22α×2β=2αβ=4×(41)=1So the quadratic  polynomial will bex2−(−2)x−1=0⇒x2+2x+1=0Option B is correct answer.

Step-by-step explanation:

HOPE IT HELPS

FOLLOW ME

MARK AS BRAINLIEST