Question

if the zeros of a cubic polynomial f x is equal to K x cube minus 8 x square + 5 are Alpha minus beta, alpha a
nd alpha + beta then find the value of k​

Answer 1

Given: Cubic polynomial f(x) = kx³ - 8x² + 5 = 0

To find:  Value of k?

Solution:

• Now the cubic polynomial is: kx³ - 8x² + 5 = 0

• The roots are α - β, α and α + β.

• So sum of zeroes are: 3α = 8/k  

           α = 8/3k  .......(i)

• Product of zeroes: α(α - β)(α + β) = -5/k

           α(α²-β²) = -5/k .......(ii)

• and (α - β)α + α(α + β) + (α + β)(α - β) = 0

           α² + α² + α² - β² = 0

           3α² = β²

          √3a = β

• Putting value of β in ii, we gwt:

           α(α²-3α²) = -5/k

           8/3k (-2α²) = -5/k

           α² = 15/16

           α = √15/4

          √3(√15/4) = β

           β = 3√5/4

• So value of k is: 8/3α

           = 32/3(√15)

Answer:

           So the value of k is 32/3(√15).

Answer 2

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