Alg2 Un4Wk5 - Fundamental theorem of algebra

Fundamental theorem of algebra

Fill in the Blank

What is the degree of

$$f\left(x\right)=3x^3-2x^2+5x-1$$  

Fill in the Blank

How many solutions (zeros) does the equation

$$0=4x^2+2x-1$$  have?

Multiple Select

What KIND of solutions (zeros) could the equation

$$0=4x^2+2x-1$$  have?

• 2 imaginary

• 2 real solutions

• one imaginary, one real

• none of these are correct

Fill in the Blank

How many zeros does the function

$$g\left(x\right)=x^4-8x-2$$  have?

Multiple Select

What kinds of zeros could the function

$$g\left(x\right)=x^4-8x-2$$  have?

• 4 real solutions

• 4 imaginary solutions

• 2 imaginary; 2 real

• three real; one imaginary

• three imaginary; one real

Multiple Choice

how many zeros does the function

$$h\left(x\right)=x\left(x+3\right)^2\left(x+5\right)$$  have?

• 4

• 2

• 1

• 3

Multiple Choice

How many positive real zeros could the function

$$f\left(x\right)=3x^3-4x^2+2x+1$$  have?

• 1

• 2

• 3

• 4

Multiple Choice

How many positive real zeros could the function have?

$$g\left(x\right)=-3x^4+6x^2+2x-5$$  

• 1

• 2

• 3

• 4

Multiple Choice

f is a polynomial with real coefficients and

$$2-i$$  is a zero of f, what is another solution of f(x)?

• -2 - i

• -2 + i

• 2 + i

• 2 - i

Multiple Choice

g is a polynomial function with real coefficients and

$$-2i$$  is a zero of g. What is another zero?

• 1-2i

• 1+2i

• 2i

• -2i

Multiple Choice

f is a polynomial function with real coefficients. If

$$2-\sqrt{5}i$$  is a zero of f, what is another zero of f?

• $$2+\sqrt{5}i$$  

• $$2-\sqrt{5}i$$  

• $$-2-\sqrt{5}i$$  

• $$-2+\sqrt{5}i$$  

Multiple Choice

Who is known as the "Father of Geometry"?

• Pythagoras
• Archimedes
• Euclid
• Galileo

Multiple Choice

Was arguably the greatest mathematician in history. According to legend, he corrected a mistake in his father‘s accounting at the age of 3, and found a way to quickly add up all integers from 1 to 100 at the age of 8.

• François Viète (1540 – 1603)

• Carl Friedrich Gauss (1777 – 1855)

• Fibonacci (1175 – 1250)

• Diophantus

Multiple Choice

He was a French mathematician and philosopher, and one of the key figures in the Scientific Revolution. He is credited with the creation of analytic geometry and the coordinate plane.

• René Descartes (1596 – 1650)

• Carl Friedrich Gauss (1777 – 1855)

• Augustin-Louis Cauchy (1789 – 1857)

• Joseph-Louis Lagrange (1736 – 1813)

Multiple Choice

Was an English physicist, mathematician, and astronomer, and one of the most influential scientists of all time. Was one of the inventors of calculus, built the first reflecting telescope, calculated the speed of sound, studied the motion of fluids, and developed a theory of colour based on how prisms split sunlight into a rainbow-coloured spectrum.

• Gottfried Wilhelm Leibniz (1646 – 1716)

• Joseph-Louis Lagrange (1736 – 1813)

• Joseph Fourier (1768 – 1830)

• Sir Isaac Newton (1642 – 1726)

Poll

After this review, I feel ----- about using the Fundamental Theorem of Algebra

• very good/very confident

• good/confident

• ok, I guess

• lost...I'm so lost...where am I?

• other: none of these express my thoughts/feelings