FYI, there is a quiz on 1.4-1.6
on block day!
1.6: Other Types of Equations
Warm Up:
Solve the following equation by completing the square: 4𝑡 2 − 6𝑡 + 10 = 0
Solving Polynomial Equations
1. Solve for the variable by factoring.
a. 4𝑥 3 − 12𝑥 2 − 9𝑥 + 27 = 0
This is the general form of a
polynomial equation
b. 9𝑤 3 + 8 = 4𝑤 + 18𝑤 2
Radical Equations
A radical equation is an equation in which the variable occurs under one or more
radicals (square root, cube root, etc). We typically solve these by raising both
sides of the equation to a power (sometimes more than once). Caution: this
solving method will often result in extraneous solutions, so check your answers!
2. Solve the radical equations
a. √2𝑥 + 6 − 4 = 2𝑥
b. √𝑦 + 5 − √𝑦 − 3 = 2
c. √2𝑚 + 3 + √𝑚 − 2 = 2
Equations with Rational Exponents
3. Solve for the variable.
5
a. 8𝑥 3 − 24 = 0
2
b. (𝑧 2 − 10𝑧 + 29)3 − 4 = 0
Equations That Are Quadratic in Form
An equation is quadratic in form if it can be turned into a quadratic equation by
making an appropriate substitution. Check it out:
4. Solve for each variable in the set of real numbers.
a. 𝑥 4 − 6𝑥 2 − 40 = 0
b. 𝑝6 + 11𝑝3 − 42 = 0
2
1
c. 2𝑥 3 + 7𝑥 3 − 15 = 0
d. 2𝑥 − 7√𝑥 − 30 = 0
e. (𝑥 2 − 2𝑥)2 − 11(𝑥 2 − 2𝑥) + 24 = 0
Absolute Value Equations
An absolute value equation is an equation in which the variable occurs inside an
absolute value expression. We can solve them by breaking up the equation into
two equations (except when there is no solution!).
5. Solve for the variable in the absolute value equations.
a. |𝑥| = 3
b. 2|3𝑥 − 7| + 7 = 11
c. |15𝑥 + 17| + 14 = 10
d. |−6𝑥 + 9| + 6 = 6