If Alpha, Beta Are Zeroes of x^2+5x+5, Find A Polynomial With Zeroes 1/Alpha And 1/Beta

​

1 thought on “If Alpha, Beta Are Zeroes of x^2+5x+5, Find A Polynomial With Zeroes 1/Alpha And 1/Beta<br /><br />​”

1. Step-by-step explanation:

   Given:–

   x^2+5x+5

   To find:–

   If α and β are the zeroes of x^2+5x+5 then Find a Polynomial with zeroes 1/α and 1/β?

   Solution :–

   Given quardratic polynomial is x^2+5x+5

   On Comparing this with the standard quadratic Polynomial ax^2+bx+c

   a = 1

   b= 5

   c= 5

   We know that

   Sum of the zeroes = -b/a

   => α + β = -5/1

   α + β = -5 ——-(1)

   Product of the zeroes = c/a

   α β = 5/1

   α β = 5———(2)

   We know that

   The Quadratic Polynomial whose zeroes (1/α) and (1/β) is K[x^2-[(1/α)+(1/β)]x+(1/α)(1/β)]

   => K[x^2-{(α + β)/α β}x +(1/α β)]

   =>K[x^2-(-5/5)x+(1/5)]

   =>K[x^2-(-1)x+(1/5)]

   =>K[x^2+x+(1/5)]

   => K[5x^2+5x+1]/5

   If K = 5 then

   => 5[5x^2+5x+1]/5

   =>5^2+5x+1

   Answer:–

   The required quardratic polynomial is 5^2+5x+1

   Used formulae:–

   • The standard quadratic Polynomial ax^2+bx+c

   • Sum of the zeroes = -b/a

   • Product of the zeroes = c/a

   • The Quadratic Polynomial whose zeroes α and β is K[x^2-(α+β)x+αβ]

   Reply