State the number of real zeros and what they are for "3x^2+5x-2" pleas help me:'(

1 answer:

3 0

This can be solved by factoring.

First, set the expression equal to zero.

$3x^2+5x-2=0$

Then, find two the factors of $ac$ whose sum is $b$ .

$6, -1$

Split $b$ into these two factors.

$3x^2+6x-x-2=0$

Next, factor by grouping.

$3x(x+2)-1(x+2) = (3x-1)(x+2) = 0$

By the Zero Product Property, set each factor equal to zero.

$3x-1 = 0 \\ x = 1/3$

$x+2=0 \\ x = -2$

These are the solutions. The Complex Conjugate Root Theorem and the Fundamental Theorem of Algebra both state that, in essence, real and imaginary solutions come in pairs of two and every polynomial of degree $n$ has exactly $n$ complex roots, but real roots are also complex roots. That sounds confusing, but this just means that you're done. Your answers are -2 and 1/3. There are two real roots.

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HELP ASAP FOR BRAINLIEST!

salantis [7]

Answer:

make sure calculator is in "radians" mode
use the cos⁻¹ function to find cos⁻¹(.23) ≈ 1.338718644

Step-by-step explanation:

A screenshot of a calculator shows the cos⁻¹ function (also called arccosine). It is often a "2nd" function on the cosine key. To get the answer in radians, the calculator must be in radians mode. Different calculators have different methods of setting that mode. For some, it is the default, as in the calculator accessed from a Google search box (2nd attachment).

The third attachment shows a graph of the cosine function (red) and the value 0.23 (dashed red horizontal line). Everywhere that line intersects the cosine function is a value of A such that cos A = 0.23. There are an infinite number of them. You need to know about the symmetry and periodicity of the cosine function to find them all, given that one of them is A ≈ 1.339.

The solution in the 4th quadrant is at 2π-1.339, and additional solutions are at these values plus 2kπ, for any integer k.

Also in the third attachment is a graph of the inverse of the cosine function (purple). The dashed purple vertical line is at x=0.23, so its intersection point with the inverse function is at 1.339, the angle at which cos(x)=0.23. The dashed orange graph shows the inverse of the cosine function, but to make it be single-valued (thus, a function), the arccosine function is restricted to the range 0 ≤ y ≤ π (purple).

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So, the easiest way to answer the problem is to use the inverse cosine function (cos⁻¹) of your scientific or graphing calculator. (Always make sure the angle mode, degrees or radians, is appropriate to the solution you want.) Be aware that the cosine function is periodic, so there is not just one answer unless the range is restricted.

I keep myself "unconfused" by reading cos⁻¹ as the angle whose cosine is. As with any inverse functions, the relationship with the original function is ...

cos⁻¹(cos A) = A

cos(cos⁻¹ a) = a