Answer:
To find the other zeros of a polynomial function given one zero, you can use synthetic division or long division to divide the given polynomial by the linear factor (x - c), where c is the given zero. By performing the synthetic division and solving the resulting quadratic function, the other zeros of the polynomial function can be found.
Explanation:
To find the other zeros of a polynomial function given one zero, you can use synthetic division or long division to divide the given polynomial by the linear factor (x - c), where c is the given zero. Let's use synthetic division to solve the given polynomial functions:
f(x) = x³ + 3x² – 34x + 48; Given zero: 3.
- Start synthetic division by writing the given zero as a divisor and the coefficients of the polynomial as the dividend. Perform the synthetic division to get the quotient, which is the quadratic function (x² + 6x - 16) and the remainder. The other two zeros can be found by solving the quadratic function.
- By solving the quadratic function, the other two zeros are approximately -6.928 and 0.928.
f(x) = x³ + 2x² – 20x + 24; Given zero: -6.
- Perform synthetic division to get the quotient: (x² + 8x + 4) and the remainder. Solve the quadratic function to find the other two zeros, which are approximately -2.82 and 0.82.
f(x) = 2x³ + 3x² – 3x – 2; Given zero: -2.
- Use synthetic division to get the quotient: (2x² - x + 1) and the remainder. Solve the quadratic function to find the other two zeros, which are approximately 0.5 + 0.866i and 0.5 - 0.866i.
f(x) = 3x³ – 16x² + 3x + 10; Given zero: 5.
- Perform synthetic division to get the quotient: (3x² - x - 2) and the remainder. Solve the quadratic function to find the other two zeros, which are approximately 2.677 and -1.01.