If (x^2 -10) is one of the factors, that can be further factored into: (x - sqrt(10) ) * (x+sqrt(10)) =0 making 2 of the 4 solutions equal: 3.1623 and -3.1623
I then used an algebraic long division calculator http://calculus-calculator.com/longdivision/ to calculate: <span>x^4 + 5x^3 ‒ x^2 ‒ 50x ‒ 90 divided by x^2 -10 which equals
</span>x^2 + 5x + 9
Using the quadratic formula, the roots of that equation are: x = -5 + sqrt (-11) / 2 and x = -5 - sqrt (-11) / 2
Both of those roots are not real.
I tried using online graphing calculators for x^4+5x^3-x^2-50x-90=0 but none worked.
2. For this equation, <span>3x^2 ‒ 8x + k = 0 I used my OWN quadratic formula calculator http://www.1728.org/quadratc.htm and found that real roots no longer exist after "k" is greater than 5.3
