Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

$x^3+2x^2+3x+4=0$

View step-by-step help

View step-by-step help

Add three or more integers

Full solution

Q.

x^3+2x^2+3x+4=0

Recognize cubic equation: Recognize that the equation $x^3 + 2x^2 + 3x + 4 = 0$ is a cubic equation, which means it will have at least one real root.
Apply Rational Root Theorem: Attempt to find rational roots using the Rational Root Theorem, which suggests that any rational root, expressed as a fraction $\frac{p}{q}$ , is such that $p$ is a factor of the constant term ( $4$ ) and $q$ is a factor of the leading coefficient ( $1$ ).
List possible rational roots: List the possible rational roots: $\pm 1$ , $\pm 2$ , $\pm 4$ .
Test rational roots: Use synthetic division or direct substitution to test the possible rational roots.
No rational roots found: After testing, we find that none of the listed rational roots satisfy the equation, meaning there are no rational roots.
Use advanced techniques: Since there are no rational roots, we can either use numerical methods or factorization techniques to approximate the roots or find exact complex roots. However, this step requires more advanced techniques such as the use of the cubic formula, graphing, or numerical solvers, which are beyond the scope of simple step-by-step calculation.

More problems from Add three or more integers

Question

9p + 6p - 8p - 2p

Posted 2 months ago

Question

Write the sentence as an equation.

\newline

3

8

x

\newline

Type a slash ( / ) if you want to use a division sign.

\newline

Posted 3 months ago

Question

Write the sentence as an equation.

\newline

7

10

, then multiply the result by

y

\newline

Type a slash ( / ) if you want to use a division sign.

\newline

Posted 3 months ago

Question

Write the sentence as an equation.

\newline

9

3

, then subtract

z

from the result.

\newline

Type a slash ( / ) if you want to use a division sign.

\newline

Posted 3 months ago

Question

Write the sentence as an equation.

\newline

4

2

v

\newline

Type a slash ( / ) if you want to use a division sign.

\newline

Posted 3 months ago

Question

Write the sentence as an equation.

\newline

5

7

, then divide the result by

u

\newline

Type a slash ( / ) if you want to use a division sign.

\newline

Posted 3 months ago

Question

Write the sentence as an equation.

\newline

210

is equal to the quotient of

v

10

\newline

Type a slash ( / ) if you want to use a division sign.

\newline

Posted 3 months ago

Question

8 + 32

Posted 2 months ago

Question

8 + 32

Posted 2 months ago

Question

\newline

4 \div 4 + 2

\newline

Posted 2 months ago