This follows from the argument principle. We integrate over the D shaped curve which starts from the positive imaginary axis say iA, down the imaginary axis to -iA and then by a semicircle back ...

I assume that a,b ar real. Suppose that a^2+b^2<8 and the polynomial has the real root \xi. It follows that: 0=\xi^4 + a\xi^3 + 2\xi^2 + b\xi + 1>\xi^4 + a\xi^3 + \frac{a^2+b^2}{4}\xi^2 + b\xi + 1=\xi^2\left(\xi+\frac{a}{2}\right)^2+\left(\frac{b}{2}\xi+1\right)^2 ...

-4x5(11x3+2x2+9x+1) Final result : -22x5 • (11x3 + 2x2 + 9x + 1) Step by step solution : Step  1  :Equation at the end of step  1  : 0-((4•(x5))•((((11•(x3))+2x2)+9x)+1)) Step  2  :Equation at the ...

There are a few key principles required to solve this problem: The derivative of a sum of functions is equal to the sum of the derivatives of each function. Power Rule:\dfrac{d}{dx} x^n = nx^{n-1} ...

\displaystyle{{x}_{{1}}^{{8}}}+{{x}_{{2}}^{{18}}}+{{x}_{{3}}^{{28}}}+{{x}_{{4}}^{{38}}}=-{1} Explanation: Given: \displaystyle{p}{\left({x}\right)}={x}^{{4}}+{x}^{{3}}+{x}^{{2}}+{x}+{1} ...

(56x3+54x2+74x+16)=0 Three solutions were found :  x = -1/4 = -0.250  x =(-5-√-199)/14=(-5-i√ 199 )/14= -0.3571-1.0076i  x =(-5+√-199)/14=(-5+i√ 199 )/14= -0.3571+1.0076i Step by step solution : ...