1-Determine the number of solutions of the equation in the complex number system. x6 + 2x2 + 14 = 0 2-Use the discriminant to determine the number of real solutions of the quadratic equation. 5x2 − x − 3 = 0 3- Use the discriminant to find the number of real and imaginary solutions of the quadratic equation. 1/4x2 − 5x + 25 = 0 real solutions imaginary solutions 4-Write the polynomial as a product of linear factors. f(x) = x2 − x + 72 f(x) = Find all the zeros of the function. (Enter your answers as a comma-separated list.) x = 5-Use the given zero to find all the zeros of the function. (Enter your answers as a comma-separated list. Include the given zero in your answer.) Function Zero g(x) = 3x3 + 23x2 + 43x − 17 −4 + i 6-Find a polynomial function with real coefficients that has the given zeros. (There are many correct answers.) 7, 7, 1 + i f(x) = 7-Find a cubic polynomial function f with real coefficients that has the given complex zeros and x-intercept. (There are many correct answers.) Complex Zeros x-Intercept x = −1 ± √5i (−5, 0) 8- Write the polynomial as the product of linear factors. f(x) = 2x3 − x2 + 16x − 8
1-Determine the number of solutions of the equation in the complex number system. x6 + 2x2 + 14 = 0 2-Use the discriminant to determine the number of real solutions of the quadratic equation. 5x2 − x − 3 = 0 3- Use the discriminant to find the number of real and imaginary solutions of the quadratic equation. 1/4x2 − 5x + 25 = 0 real solutions imaginary solutions 4-Write the polynomial as a product of linear factors. f(x) = x2 − x + 72 f(x) = Find all the zeros of the function. (Enter your answers as a comma-separated list.) x = 5-Use the given zero to find all the zeros of the function. (Enter your answers as a comma-separated list. Include the given zero in your answer.) Function Zero g(x) = 3x3 + 23x2 + 43x − 17 −4 + i 6-Find a polynomial function with real coefficients that has the given zeros. (There are many correct answers.) 7, 7, 1 + i f(x) = 7-Find a cubic polynomial function f with real coefficients that has the given complex zeros and x-intercept. (There are many correct answers.) Complex Zeros x-Intercept x = −1 ± √5i (−5, 0) 8- Write the polynomial as the product of linear factors. f(x) = 2x3 − x2 + 16x − 8
1-Determine the number of solutions of the equation in the complex number system. x6 + 2x2 + 14 = 0 2-Use the discriminant to determine the number of real solutions of the quadratic equation. 5x2 − x − 3 = 0 3- Use the discriminant to find the number of real and imaginary solutions of the quadratic equation. 1/4x2 − 5x + 25 = 0 real solutions imaginary solutions 4-Write the polynomial as a product of linear factors. f(x) = x2 − x + 72 f(x) = Find all the zeros of the function. (Enter your answers as a comma-separated list.) x = 5-Use the given zero to find all the zeros of the function. (Enter your answers as a comma-separated list. Include the given zero in your answer.) Function Zero g(x) = 3x3 + 23x2 + 43x − 17 −4 + i 6-Find a polynomial function with real coefficients that has the given zeros. (There are many correct answers.) 7, 7, 1 + i f(x) = 7-Find a cubic polynomial function f with real coefficients that has the given complex zeros and x-intercept. (There are many correct answers.) Complex Zeros x-Intercept x = −1 ± √5i (−5, 0) 8- Write the polynomial as the product of linear factors. f(x) = 2x3 − x2 + 16x − 8
1-Determine the number of solutions of the equation in the complex number system.
x6 + 2x2 + 14 = 0
2-Use the discriminant to determine the number of real solutions of the quadratic equation.
5x2 − x − 3 = 0
3-
Use the discriminant to find the number of real and imaginary solutions of the quadratic equation.
1/4x2 − 5x + 25 = 0
real solutions imaginary solutions
4-Write the polynomial as a product of linear factors.
f(x) = x2 − x + 72 f(x) =
Find all the zeros of the function. (Enter your answers as a comma-separated list.) x = 5-Use the given zero to find all the zeros of the function. (Enter your answers as a comma-separated list. Include the given zero in your answer.)
Function
Zero
g(x) = 3x3 + 23x2 + 43x − 17
−4 + i
6-Find a polynomial function with real coefficients that has the given zeros. (There are many correct answers.)
7, 7, 1 + i
f(x) =
7-Find a cubic polynomial function f with real coefficients that has the given complex zeros and x-intercept. (There are many correct answers.)
Complex Zeros x-Intercept x = −1 ± √5i (−5, 0)
8-
Write the polynomial as the product of linear factors.
f(x) = 2x3 − x2 + 16x − 8
Combination of a real number and an imaginary number. They are numbers of the form a + b , where a and b are real numbers and i is an imaginary unit. Complex numbers are an extended idea of one-dimensional number line to two-dimensional complex plane.
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