How many real roots and how many complex roots exist for the polynomial f(x)=x^4+x^3-5^x+x-6?

To prove "p is equal to q" using an indirect proof, what would your starting assumption be?

Asays "we are both knaves" and b says nothing. exercises 24–31 relate to inhabitants of an island on which there are three kinds of people: knights who always tell the truth, knaves who always lie, and spies (called normals by smullyan [sm78]) who can either lie or tell the truth. you encounter three people, a, b, and c. you know one of these people is a knight, one is a knave, and one is a spy. each of the three people knows the type of person each of other two is. for each of these situations, if possible, determine whether there is a unique solution and determine who the knave, knight, and spy are. when there is no unique solution, list all possible solutions or state that there are no solutions. 24. a says "c is the knave," b says, "a is the knight," and c says "i am the spy."

Players on the school soccer team are selling candles to raise money for an upcoming trip. each player has 24 candles to sell. if a player sells 4 candles a profit of$30 is made. if he sells 12 candles a profit of $70 is made