The roots of the cubic polynomial are 1, (5+√17)/2, and (5-√17)/2 options (C), (D), and (F) are correct.
What is polynomial?
Polynomial is the combination of variables and constants systematically with "n" number of power in ascending or descending order.
[tex]\rm a_1x+a_2x^2+a_3x^3+a_4x^4..........a_nx^n[/tex]
We have a cubic or third-degree polynomial:
F(x) = x³ - 6x² + 7x - 2
To find the all possible roots of the cubic polynomial
By using the trial and error method:
Plug x = 1
F(1) = 1 - 6 + 7 - 2
F(1) = 8 - 8
F(1) =0
x = 1 is one of the roots of the polynomial.
We can write the cubic polynomial in the factored form:
F(x) = (x - 1)(x² -5x + 2)
We have a quadratic polynomial:
= x² -5x + 2
To find the roots of the quadratic polynomial use the quadratic formula:
a= 1, b = -5, and c =2
[tex]\rm x = \dfrac{-b \pm\sqrt{b^2-4ac}}{2a}[/tex]
[tex]\rm x = \dfrac{-(-5) \pm\sqrt{(-5)^2-4(1)(2)}}{2(1)}[/tex]
After solving:
x = (5+√17)/2
x = (5-√17)/2
Thus, the roots of the cubic polynomial are 1, (5+√17)/2, and (5-√17)/2 options (C), (D), and (F) are correct.
Learn more about Polynomial here:
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