The sum of The zeroes of cubic ploymoial p(x)=2x³-17x²+38x-15
Answers
Sum of the zeroes is 17/2.
Formula:
Let us consider a n-th degree polynomial
f(x) = a₀xⁿ + a₁xⁿ⁻¹ + a₂xⁿ⁻² + a₄xⁿ⁻³ + ... + aₙ
with a₀ ≠ 0 and the coefficients being real or complex.
Let α₁, α₂, α₃, ..., αₙ be the roots of f(x) = 0; we can write
α₁ + α₂ + α₃ + ... + αₙ = - a₁/a₀
α₁ α₂ + α₁ α₃ + ... + α₁ αₙ + α₂ α₃ + ... = a₂/a₀
... ... ... ... ...
α₁ α₂ α₃ ... αₙ = (- 1)ⁿ aₙ/a₀
Which can be shortened as
Σ α₁ = - a₁/a₀
Σ α₁ α₂ = a₂/a₀
... ... ...
α₁ α₂ ... αₙ = (- 1)ⁿ aₙ/a₀
Specific case of 3 degree polynomial:
If f(x) = a₀x³ + a₁x² + a₂x + a₃ be a trinomial and α, β, γ be its zeroes, then
α + β + γ = - a₁/a₀
αβ + βγ + γα = a₂/a₀
αβγ = - a₃/a₀
Solution:
The given polynomial is
p(x) = 2x³ - 17x² + 38x - 15
Using the relation between zeroes and coefficients, we can find the sum of the zeroes of the given polynomial
= - (- 17)/2 = 17/2
Related question:
Given that the zeroes of the cubic polynomial x³ - 6x² + 3x + 10 are of the form a, a + b, a + 2b for some real numbers a and b, find the values of a and b as well as the zeroes of the given polynomial. - https://brainly.in/question/15823539