If zeroes of cubic polynomial f(x)=kx^3-8x^2+5 are a-b,a,a+b find the

1.	If zeroes of cubic polynomial f(x)=kx^3-8x^2+5 are a-b,a,a+b find the value of k?
Answer» k = 8/3αα = √15 / 4Step-by-step explanation:f(x) = kx³ - 8x² + 5\xa0Roots are α - β , α & α +βSum of roots = - (-8)/k Sum of roots = α - β + α + α +β = 3α=> 3α = 8/k=> k = 8/3α\xa0or we can solve as below\xa0f(x) = (x - (α - β)(x - α)(x - (α +β))= (x - α)(x² - x(α+β + α - β) + (α² - β²))= (x - α)(x² - 2xα + (α² - β²))= x³ - 2x²α + x(α² - β²) - αx² +2α²x - α³ + αβ²= x³ - 3αx² + x(3α² - β²) + αβ² - α³= kx³ - 3αkx² + xk(3α² - β²) + k(αβ² - α³)\xa0comparing withkx³ - 8x² + 5\xa0k(3α² - β²) = 0 => 3α² = β²k(αβ² - α³) = 5=>k(3α³ - α³) = 5=> k2α³ = 5\xa03αk = 8 => k = 8/3α(8/3α)2α³ = 5=> α² = 15/16=> α = √15 / 4

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