SOLUTION: I'm being asked to solve for x (find the roots) of this equation: {{{ 3x^3+2x^2+75x-50=0 }}} I've tried factor theorem but I can't get it to equal 0. I tried factoring by g

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: I'm being asked to solve for x (find the roots) of this equation: {{{ 3x^3+2x^2+75x-50=0 }}} I've tried factor theorem but I can't get it to equal 0. I tried factoring by g      Log On


   

Question 1132136: I'm being asked to solve for x (find the roots) of this equation:
+3x%5E3%2B2x%5E2%2B75x-50=0+

I've tried factor theorem but I can't get it to equal 0. I tried factoring by grouping but I can't make that work because of the sign on the last term. Help please?
Found 3 solutions by josgarithmetic, MathLover1, ikleyn:
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
3x%5E3%2B75x%2B2x%5E2-50=0

3%28x%5E3%2B25x%29%2B2%28x%5E2-25%29=0

3x%28x%5E2%2B25%29%2B2%28x%5E2-25%29=0

If Rational Root Theorem did not help, either try a numerical method or a graphing tool. There is one real root near about 0.65.

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

3x%5E3%2B2x%5E2%2B75x-50=0++

use Newton-Raphson
x%5Bn%2B1%5D=x%5Bn%5D-f%28x%29%2Ff%92%28x%29
f’%28x%29=9x%5E2%2B4x%2B75

Let x%5B1%5D+=1
than x%5B2%5D+=1-%283%2A1%5E3%2B2%2A1%5E2%2B75%2A1-50%29%2F%289%2A1%5E2%2B4%2A1%2B75%29
x%5B2%5D+=1-%283%2B2%2B75-50%29%2F%289%2B4%2B75%29
x%5B2%5D+=1-30%2F88
+x%5B2%5D+=88%2F88-30%2F88
+x%5B2%5D+=58%2F88
x%5B2%5D+=0.659091


x%5B3%5D=0.659091-%281.159556154817871713%29%2F%2881.545972516529%29
x%5B3%5D=0.659091-0.01422
x%5B3%5D ≈ 0.644871=> one real solution

you also have complex roots:
x≈-0.6558+-+5.0414%2A+i
x≈-0.6558+%2B5.0414+%2Ai

Answer by ikleyn(52798) About Me  (Show Source):
You can put this solution on YOUR website!
.

            I used the polynomial roots finder from the site

            https://www.mathportal.org/calculators/polynomials-solvers/polynomial-roots-calculator.php

            Below are the results from this site:


Result 

The roots of the polynomial  3x^3 + 2x^2 + 75 - 50  are:


    x1 = 0.64485

    x2 = −0.65576+5.0414∗i

    x3 = −0.65576−5.0414∗i


Explanation

This polynomial has no rational roots that can be found using Rational Root Test.

Roots were found using qubic formulas.


If you want to get more results/explanations, go to this site and explore it . . .