Answer:
The polynomial is [tex]x^{3} - 1.46x^{2} - 3.93x + 6[/tex]
Step-by-step explanation:
A nth order polynomial f(x) has roots [tex]x_{1}, x_{2}, ..., x_{n}[/tex] such that [tex]f(x) = (x - x_{1})*(x - x_{2})*...*(x - x_{n}}[/tex],
Which of the following is a polynomial with roots: − square root of 3 , square root of 3, and −2?
So
[tex]x_{1} = x_{2} = \sqrt{3}[/tex]
[tex]x_{3} = -2[/tex]
Then
[tex](x - \sqrt{3})^{2}*(x - (-2)) = (x - \sqrt{3})^{2}*(x + 2) = (x^{2} -2x\sqrt{3} + 3)*(x + 2) = x^{3} + 2x^{2} - 2x^{2}\sqrt{3} - 4x\sqrt{3} + 3x + 6[/tex]
Since [tex]\sqrt{3} = 1.73[/tex]
[tex]x^{3} + 2x^{2} - 3.46x^{2} - 6.93x + 3x + 6 = x^{3} - 1.46x^{2} - 3.93x + 6[/tex]
The polynomial is [tex]x^{3} - 1.46x^{2} - 3.93x + 6[/tex]
