Solving Quadratic Equations

Factoring

100

The roots of the quadratic equation 2x²+x-6=0

What is x=-2 or x=3/2? 

200

The roots of the quadratic equation x²+4x=0

What is x=0 or x=-4?

300

The Zero Product Property states

What is if (a)(b)=0, then a=0 or b=0?

400

The solutions of the quadratic equation 3b³-5b²+2b

What is b=0, b=2/3, or b=1?

500

The roots of the quadratic equation 9r²-5r-10

What is unknown because the equation is not factorable?

Square Root Method

100

The solutions of the equation -5x²=-500

What is x=10 or x=-10?

200

The roots of the equation m²+7=88

What is x=9 or x=-9?

300

The roots of the equation -2+3(x-4)²=13

What is x=4+√5 or x=4-√5?

400

The Square Root Property states

What is if x²=a, then x=+/- √a?

500

The roots of the equation (5x+1)²-24=-25

What is x=-1/5 +/- (i/5)?

Quadratic Formula

100

To use the quadratic formula, the first step is

What is writing the equation in standard form (setting the equation equal to zero)?

200

The discriminant is

What is the expression b2-4ac?

300

The roots of the equation 2x²-3x-15=5

What is x=4 or x=-5/2?

400

The roots of the equation k²-31-2k=-6-3k²-2k

What is x=5/2 or x=-5/2?

500

The solutions of the equation 8n²+7n-15=-7

What is x=(-7/16) +/- (√305)/16?

Completing the Square

100

The first step to solving the quadratic equations using completing the square

What is to get all the x terms on the left hand side and the constants (numbers) on the right hand side)?

200

The value added to both sides to complete the square for the equation x²-(7/2)x=-6

What is 49/16?

300

The solutions of the equation x2-12x+11=0

What is x=1 or x=11?

400

The solutions of the equation k2-4k+1=-5

What is x=2 +/- i√2?

500

The roots of the equation 2x²-5x+67=0

What is x= (5 +/- i√511)/4

Find the Discriminant

100

The number of solutions of a quadratic equation if the discriminant is 3

What are 2 real roots?

200

The number and type of solutions of the equation 2x²+16x+33=0

What are two nonreal roots (imaginary roots)?

300

The number and type of solutions of the equation 9x²-12x+4=0

What is one real root?

400

The number and type of solutions of the equation x2-5x+6=0

What is two real roots?

500

Challenge: The discriminant of a quadratic equation is 45, the roots are (be precise)

What is two irrational roots?