Suppose that a polynomial function of degree 4 with rational coefficients has i and (-3 + square root of 3)as zeros find the other zeros
There must be four roots total and complex numbers have conjugates that are roots. One other root is therefore
If -3 + sqrt3, is a root, the another root is -3 - sqrt3, as a consequence of the +/-sqrt(b^2 - 4ac) in the quadratic equation.
The polynomial must be a multiple of
(x^2 +1)(x +3 -sqrt3)(x +3 +sqrt3) = 0
(x^2+1)[(x+3)^2 -3] = 0
(x^2+1)(x^2 +6x +6) = 0
x^4 +6x^3 +7x^2 +6 = 0
Answer this Question
Find a polynomial of the specified degree that satisfies the given conditions. Degree 4; zeros −3, 0, 1, 4; coefficient of x3 is 4
- asked by Jillian
- 2,595 views
A cubic polynomial function f is defined by f(x) = 4x^3 + ax^2 + bx + k? A cubic polynomial function f is defined by: f(x) = 4x^3 + ax^2 + bx + k where a, b, and k are constants. The function f has a local minimum at x= -1, and the graph of f has a point
- asked by Leanna
- 2,976 views
Consider the polynomial: f(x) = 2x^3 – 3x^2 – 8x – 3. (a) By using the Rational Zero Theorem, list all possible rational zeros of the given polynomial. (b) Find all of the zeros of the given polynomial. Be sure to show work, explaining how you have
- asked by Alyssa
- 806 views
1. which of the following is a fourth degree polynomial function? select all that apply. a. f(x)= 4x^3 - x^2 + 2x - 7 b. f(x)= 5-x^4 c. f(x)= 1 / 2x^4 + x^2 -5 d. f(x)= 3x^4 + 2x^3 -4x +1 2. which function below has the end behavior f(x) approaches neg.
- asked by mr mango
- 4,851 views
1.is the function f(X)=4-7x^5 a polynomial function? if so state its degree and leading coefficient. 6.use the remainder theorem to determine if x-2 is a factor of the polynomial f(x)=3x^5-7x^3-11x^2+2
- asked by samantha
- 2,441 views
Use the rational root theorem to list all possible rational roots for the equation. X^3+2x-9=0. Use the rational root theorem to list all possible rational roots for the equation. 3X^3+9x-6=0. A polynomial function P(x) with rational coefficients has the
- asked by Chelsey
- 13,588 views
Determine the maximum and minimum number of turning points for the function h(x) = -2x^4 - 8x^3 + 5x -6. Maximum:3 Minimum:1 Is this a valid reason: A quartic polynomial function has a 3 Turning points. The turning point is always 1 less than the degree.
- asked by Melinda
- 5,423 views
Find a polynomial with integer coefficients that satisfies the given conditions. P has degree 2 and zeros 2 + i and 2 − i.
- asked by Drue
- 1,797 views
Three zeroes of a fifth degree polynomial function are 1/3, 4 - 6i, and -2 + 11i. Determine the remaining zeroes of the function. 4 + 6i, -2 - 11i -1/3, 4 + 6i, 2 + 11i -4 + 6i, 2 - 11i 3, 4 + 6i, -2 - 11i Can I have some guidance for this please? I am
- asked by Max
- 1,652 views
Find a polynomial with integer coefficients that satisfies the given conditions. R has degree 4 and zeros 3 − 4i and 5, with 5 a zero of multiplicity 2.
- asked by Kyle
- 2,446 views
what is the general relationship between the degree of a polynomial function and the number of "bends" or relative maximum and minimum points in the graph?
- asked by Lauren
- 1,479 views
write a fourth degree polynomial function a leading coefficient o 1 given three of its zeros are -1, 3 and 2i, then re-write it in simplified form.
- asked by Piggy
- 936 views
A polynomial function f(x) with real coefficients has the given degree, zeros, and solution point. Degree: 3 Zeros: -2,2+2√2i Solution Point: f(−1) = −68 (a) Write the function in completely factored form. (b) Write the function in polynomial form.
- asked by Ben Dover III
- 4,470 views
Which of the following statements about a polynomial function is false? 1) A polynomial function of degree n has at most n turning points. 2) A polynomial function of degree n may have up to n distinct zeros. 3) A polynomial function of odd degree may have
- asked by Muneer
- 5,013 views
form a polynomial f(x) with real coefficients having the given degree and zeros. Degree 4; zeros:-3 +5i; 2 multiplicity 2 enter the polynomial f(x)=a(?)
- asked by Heather
- 4,804 views
Fine a third degree polynomial function f(x) with real coefficients that has 4 and 2i are zeros and such that f(-1) =-50 4 21 -2i (x-4)(x-2i)(x+2i) (x-4)(x2+4) x3-16+4x-4x2 (x3-4x2+4x-16) -50=a(-1-4-4-16) -50=.25 a=2 Not understanding, please help
- asked by Sally
- 1,149 views
A polynomial f(x) with real coefficients and leading coefficient 1 has the given zeros and degree. Express f(x) as a product of linear and/or quadratic polynomials with real coefficients that are irreducible over . 3, −3 − 2i; degree 3
- asked by deena
- 1,709 views
Gr.11 - Rational functions graphing.
1. Identify a rational function whose graph is a horizontal line except for two holes. Graph the function. 2. Identify a rational function who graph lies entirely above the x-axis and has a single vertical asymptote. Graph the function. 3. Identify a
- asked by Mae
- 2,163 views
Explain why a polynomial function with an odd degree must have at least one real zero
- asked by Wren
- 1,335 views
Find a polynomial function P of the lowest possible degree, having real coefficients, a leading coefficient of 1, and with the given zeros. 2plus2i, minus1, and 2
- asked by Peter Asiedu
- 1,760 views