a. The equation -9x+4x^2+2=0 has two solutions because it is a quadratic equation, and the Fundamental Theorem of Algebra states that a quadratic equation can have at most two solutions.
b. The equation -2x^2-5=0 has two solutions because it is a quadratic equation, and the Fundamental Theorem of Algebra states that a quadratic equation can have at most two solutions.
c. The equation 5/7x^2=0 has only one solution because it factors into (5/7)x(x) = 0, so x=0 is the only solution.
d. The equation 0x^2+7x-2=0 has two solutions because it is a linear equation (degree of 1) and the Fundamental Theorem of Algebra states that a linear equation can have at most one solution.
e. The equation 0x^3-x^2+2x+4=0 has three solutions because it is a cubic equation (degree of 3) and the Fundamental Theorem of Algebra states that a cubic equation can have at most three solutions.
Use the Fundamental Theorem of Algebra to determine which of the following equations have two solutions. Explain your reasoning in 1-2 sentences.
a. -9x+4x^2+2=0
b. -2x^2-5=0
c. 5/7x^2=0
d. 0x^2+7x-2=0
e. 0x^3-x^2+2x+4=0
1 answer