Question

Please help me with this.

Answer 1

Using division and the graph, the zeroes of the function are given as follows:

• x = -1 with multiplicity 2.

• x = 2/3 with multiplicity 1.

How do we find all the zeros of the function?

The function in this problem is defined as follows:

f(x) = -3x³ -4x² + x + 2.

From the graph, we have that x = -1 is a zero of the function, meaning that it can be written as follows:

-3x³ -4x² + x + 2 = (x + 1)(ax² + bx + c).

The other zeros will be the zeros of ax² + bx + c. To find the coefficients, we use a system of equations, hence:

(x + 1)(ax² + bx + c) = -3x³ -4x² + x + 2

ax³ + (a + b)x² + (c + b)x + c = 2.

Hence the coefficients are given by:

• a = -3.

• c = 2.

• a + b = -4 -> b = -1.

Thus the quadratic equation that we have to solve is:

-3x² - x + 2 = 0

3x² + x - 2 = 0.

Hence:

• $\Delta = 1^2-4(3)(-2) = 25$

• $x_1 = \frac{-1 + \sqrt{25}}{6} = \frac{2}{3}$

• $x_2 = \frac{-1 - \sqrt{25}}{6} = -1$

The zeroes of the function are given as follows:

• x = -1 with multiplicity 2.

• x = 2/3 with multiplicity 1.

More can be learned about the zeroes of a function at brainly.com/question/65114

#SPJ1