polynomial equations

• If f(X) = anxn + an-1xn-1+ …..+a2x2 + a1x+a0 then the factors of the constant (a0) divided by the factors of Lc (an) always give you rational solutions (roots)

• rational root theorem

• irrational conjugates theorem

• fundamental theorem of algebra

• descartes rule of signs

p equals

• a factor of last term

• a factor of first term

q equals

• a factor of last term

• a factor of first term

• Let f be a polynomial function with rational coefficients, and let a and b be rational numbers such that √b is irrational. If (a + √b) is zero of f, then (a - √b) is also a zero of f.

• rational root theorem

• descartes rule of signs

• irrational conjugates theorem

• fundamental theorem of algebra

how many roots does the equation (3x^2+2x+6) have?

• 1

• 3

• 4

• 2

how many solutions does the question (x^5-2x^4-3x^3+4x^2-x-1) have?

• 3 positive real solutions

• 3 or one positive real solutions

• 2 negative solutions

• 0 negative solutions

if the discriminant is equal to 0, how many solutions does the equation have

• no real solutions

• two real solutions

• one real solution

• one negative solution

Match the following as it relates to solving an equation

• set each factor to zero and solve

• 1st step

• check your answers

• 2nd step

• factor the equation

• 4th step

• set the equation equal to zero

• 3rd step