Question

f(x)=3x^(4)-26x^(3)+73x^(2)-74x+24 If the answer is not an integer, enter it as a fraction. If there are multiple zeros, separate the answer: Real zeros:

Answer 1

The given equation is a quadratic equation. We can solve it using the quadratic formula.

Step-by-step explanation:

The given equation is a quadratic equation of the form ax²+bx+c=0, where a = 1, b = 1.2 x 10^-2, and c = -6.0 x 10^-3. To solve this equation, we can use the quadratic formula: x = (-b ± √(b²-4ac)) / (2a). Plugging in the values, we have:

x = (-1.2 x 10^-2 ± √((1.2 x 10^-2)² - 4(1)(-6.0 x 10^-3))) / (2 x 1)

Simplifying this equation and solving for x will give us the values of x.

Answer 2

The real zeros of the quartic equation
`3x^4 - 26x^3 + 73x^2 - 74x + 24` are 1 and 2.78.

Step-by-step explanation:

A quadratic equation is a second-degree polynomial equation in a single variable, typically expressed as
`ax^2 + bx + c = 0,` where "x" represents the variable, and "a," "b," and "c" are constants.

The given equation is a quartic equation:

`f(x) = 3x4 - 26x3 + 73x2 - 74x + 24.`

To find the real zeros, we can factor the equation or use synthetic division to test the given options.

Using synthetic division, we find that x = 1 and x ≈ 2.78 are the real zeros.

Therefore, the real zeros of the equation are 1 and 2.78.