Question

Choose all of the zeroes of f(x). a) –3 with multiplicity b) 13 with multiplicity c) 10 with multiplicity d) 10 with multiplicity e) 33 with multiplicity 0

Answer 1

The zeroes of f(x) and their multiplicities are -3, 13 (both with multiplicity 1), and 10 (with multiplicity 2).

Step-by-step explanation:

The question asks you to choose all of the zeroes of the function f(x) and their multiplicities. To determine the zeroes of a function, we need to find the values of x that make f(x) equal to zero. In this case, the possible zeroes are -3, 13, and 10. The multiplicities are given as well, which means that each zero occurs a certain number of times. The correct answers are a) –3 with multiplicity 1, b) 13 with multiplicity 1, and c) 10 with multiplicity 2. Therefore, the choices d) and e) are incorrect as they do not match the given multiplicities.

Answer 2

The zeros of the function f(x) can be found by solving the quadratic equation x² - 3x + 10 = 0. Since the discriminant is negative, there are no real roots for this equation. Therefore, the correct answer is f) 0.

Step-by-step explanation:

The zeros of the function f(x) can be found by solving the quadratic equation ax² + bx + c = 0, where a, b, and c are the coefficients of the equation.

In this case, the equation is x² - 3x + 10 = 0. The discriminant is b² - 4ac, which is equal to (-3)² - 4(1)(10) = 9 - 40 = -31.

Since the discriminant is negative, there are no real roots for this equation. Therefore, the correct answer is f) 0.