\(\textbf{1)}\) Solve for \(x\). \(\,3x^2 +4x=0 \)

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The answer is \( x=0, -\frac{4}{3} \)

 

\(\textbf{2)}\) One root is \(4\), what are the other two roots? \(x^3-5x^2+2x+8=0 \)

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The answer is \( x=-1, 2, 4 \)

 

\(\textbf{3)}\) Solve for \(x\). \(\,x^2 – 6x + 8 = 0 \)

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The answer is \( x = 2, 4 \)

 

\(\textbf{4)}\) Solve for \(x\). \(\,x^2 + 4x – 5 = 0 \)

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The answer is \( x = 1, -5 \)

 

\(\textbf{5)}\) One root is \(1\), what are the other two roots? \(x^3 – 7x^2 + 14x – 8 = 0 \)

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The answer is \( x = 1, 2, 4 \)

 

\(\textbf{6)}\) Solve for \(x\). \(\,x^2 – 3x + 2 = 0 \)

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The answer is \( x = 1, 2 \)

 

\(\textbf{7)}\) Solve for \(x\). \(\,2x^2 – 5x + 3 = 0 \)

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The answer is \( x = 1, \frac{3}{2} \)

 

\(\textbf{8)}\) Solve for \(x\). \(\,x^2 + 2x + 1 = 0 \)

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The answer is \( x = -1 \)

 

\(\textbf{9)}\) One root is \(2\), what are the other two roots? \(x^3 – 6x^2 + 11x – 6 = 0 \)

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The answer is \( x = 1, 2, 3 \)

 

 

See Related Pages\(\)

\(\bullet\text{ Adding and Subtracting Polynomials}\)
\(\,\,\,\,\,\,\,\,(4d+7)−(2d−5)…\)

\(\bullet\text{ Multiplying Polynomials}\)
\(\,\,\,\,\,\,\,\,(x+2)(x^2+3x−5)…\)

\(\bullet\text{ Dividing Polynomials}\)
\(\,\,\,\,\,\,\,\,(x^3-8)÷(x-2)…\)

\(\bullet\text{ Dividing Polynomials (Synthetic Division)}\)
\(\,\,\,\,\,\,\,\,(x^3-8)÷(x-2)…\)

\(\bullet\text{ Synthetic Substitution}\)
\(\,\,\,\,\,\,\,\,f(x)=4x^4−3x^2+8x−2…\)

\(\bullet\text{ End Behavior}\)
\(\,\,\,\,\,\,\,\, \text{As } x\rightarrow \infty, \quad f(x)\rightarrow \infty \)
\(\,\,\,\,\,\,\,\, \text{As } x\rightarrow -\infty, \quad f(x)\rightarrow \infty… \)

\(\bullet\text{ Completing the Square}\)
\(\,\,\,\,\,\,\,\,x^2+10x−24=0…\)

\(\bullet\text{ Quadratic Formula and the Discriminant}\)
\(\,\,\,\,\,\,\,\,x=-b \pm \displaystyle\frac{\sqrt{b^2-4ac}}{2a}…\)

\(\bullet\text{ Complex Numbers}\)
\(\,\,\,\,\,\,\,\,i=\sqrt{-1}…\)

\(\bullet\text{ Multiplicity of Roots}\)
\(\,\,\,\,\,\,\,\,\)\(…\)

\(\bullet\text{ Rational Zero Theorem}\)
\(\,\,\,\,\,\,\,\, \pm 1,\pm 2,\pm 3,\pm 4,\pm 6,\pm 12…\)

\(\bullet\text{ Descartes Rule of Signs}\)
\(\,\)

\(\bullet\text{ Roots and Zeroes}\)
\(\,\,\,\,\,\,\,\,\text{Solve for }x. 3x^2+4x=0…\)

\(\bullet\text{ Linear Factored Form}\)
\(\,\,\,\,\,\,\,\,f(x)=(x+4)(x+1)(x−3)…\)

\(\bullet\text{ Polynomial Inequalities}\)
\(\,\,\,\,\,\,\,\,x^3-4x^2-4x+16 \gt 0…\)