Alg 2 Lesson 22 Practice

When can you solve by factoring? Select all that apply.

• When the discriminant is a perfect square.

• When the solutions are non-real.

• When the discriminant is negative.

• When the quadratic equation is factorable.

What is the formula for the discriminant?

•  $\sqrt{b^2-4ac}$  

•  $b^2-4ac$  

•  $\frac{-b\pm\sqrt{b^2-4ac}}{2a}$  

•  $ax^2+bx+c=0$  

If the discriminant is negative, what is the number and nature of roots?

• 2 real roots

• 2 non-real roots

• 1 distinct real root

• 1 non-real root

If the discriminant is positive, what is the number and nature of roots?

• 2 real roots

• 2 non-real roots

• 1 distinct real root

• 1 non-real root

If the discriminant is zero, what is the number and nature of roots?

• 2 real roots

• 2 non-real roots

• 1 distinct real root

• 1 non-real root

When can you solve by taking the square root?

• When there is NO x term.

• When the discriminant is a perfect square.

• You can always solve by taking the square root.

• When the equation is in standard form.

Solve:

 $x^2-2=-x$  

Select ALL the solutions.

•  $x=1$  

•  $x=-2$  

•  $x=-8$  

•  $x=-1$  

•  $x=3$  

Solve:

 $7x^2-5=205$  

Select ALL the solutions.

•  $\sqrt{30}$  

•  $-\sqrt{30}$  

•  $\frac{7}{16}$  

•  $\frac{1}{4}$  

•  $-\frac{1}{4}$  

Solve:

 $4x^2-4x=48$  

Select ALL the solutions.

•  $4$  

•  $-3$  

•  $-1$  

•  $-\frac{1}{3}$  

•  $\frac{1}{3}$  

Solve:

 $5x^2-6x+9=0$  

•  $x=\frac{3+6i}{5}\ and\ x=\frac{3-6i}{5}$  

•  $x=\frac{3\sqrt{2}}{2}\ and\ x=-\frac{3\sqrt{2}}{2}$  

•  $x=3\sqrt{2}\ and\ x=-3\sqrt{2}$  

•  $x=\frac{3+3\sqrt{6}}{5}\ and\ x=\frac{3-3\sqrt{6}}{5}$