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This is an unfactorable polynomial function: -4x^5-20x^4-23x^3+42x^2+20x-8.
Can you please teach me how to solve for the x-intercepts manually without
making the graph automatically using an app. I got 3 x-intercepts from the roots
in the graph (-5.71..., 0.25..., 1.84...). Thank you so much.
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This polynomial has no rational roots that can be found using Rational Root Test.
Solution
= 0.27286, = −0.65098, = 1.08534,
= −2.85361+1.49371i, = −2.85361−1.49371i.
Explanation
This polynomial has no rational roots that can be found using Rational Root Test.
Roots were found using Newton method.
An online solver was used from web-site
https://www.mathportal.org/calculators/solving-equations/polynomial-equation-solver.php
https://www.mathportal.org/calculators/solving-equations/polynomial-equation-solver.php?val1=-4x%5E5-20x%5E4-23x%5E3%2B42x%5E2%2B20x-8&val2=0&val3=-4%7Bx%7D%5E%7B5%7D-20%7Bx%7D%5E%7B4%7D-23%7Bx%7D%5E%7B3%7D%2B42%7Bx%7D%5E%7B2%7D%2B20x-8%3D0
Notice that the found roots have nothing in common with the "roots" in your post,
so, in this part, your post is a kind of disinformation.
This equation does not allow factoring, does not allow to apply rational roots test and is of the degree 5.
Such algebraic/polynomial equations have no formulas to find their roots manually.
Only numerical solutions are possible, providing approximate values for the roots.
Did you get this assignment from your Math professor ?
Math professor should know these basic truths as firmly as he (or she) knows that 2 x 2 = 4.