The Quadratic Formula (Real and Complex)

The Quadratic Formula (Real and Complex)

By Drew Besson

Multiple Choice

Simplify.

$$\left(-1+2i\right)\div\left(-3+4i\right)$$  

• $$\frac{-12-16i}{25}$$  

• $$\frac{11-2i}{25}$$  

• $$\frac{-6i+8}{25}$$  

• $$\frac{2-14i}{25}$$  

Multiple Choice

Simplify.

$$\left(3i\right)\div\left(4-3i\right)$$  

• $$\frac{12i-9}{25}$$  

• $$\frac{3i-9}{10}$$  

• $$\frac{24+18i}{25}$$  

• $$\frac{12+9i}{25}$$  

Multiple Choice

Simplify.

$$\left(-1-3i\right)\div\left(-i\right)$$  

• $$-i+3$$  

• $$-1-3i$$  

• $$\frac{-4-3i}{2}$$  

• $$-9i$$  

The Quadratic Formula (Real and Complex Solutions)

​How do I solve quadratic equations using the quadratic formula?

​The quadratic formula is a useful tool for finding solutions, particularly when an equation cannot be factored easily.

​How do I solve quadratic equations using the quadratic formula?

​How do I solve quadratic equations using the quadratic formula?

​How do I solve quadratic equations using the quadratic formula?

Multiple Choice

Solve using the quadratic formula.

$$p^2+4p-5=0$$  

• $$\left\{1,\ -5\right\}$$  

• $$\left\{1\right\}$$  

• $$\left\{5,-2.5\right\}$$  

• $$\left\{1,\ -2.5\right\}$$  

Multiple Choice

Solve using the quadratic formula.

$$r^2-2r+4=0$$  

• $$\left\{1\right\}$$  

• $$\left\{1+i\sqrt[]{3},\ 1-i\sqrt[]{3}\right\}$$  

• $$\left\{1.618,\ -0.618\right\}$$  

• $$\left\{\frac{1+i\sqrt[]{3}}{2},\ \frac{1-i\sqrt[]{3}}{2}\right\}$$  

Multiple Choice

Solve using the quadratic formula.

$$6n^2-5n+5=0$$  

• $$\frac{5+\sqrt[]{5}}{2},\ \frac{5-\sqrt[]{5}}{2}$$  

• $$\frac{-5+i\sqrt[]{95}}{12},\ \frac{-5-i\sqrt[]{95}}{12}$$  

• $$\frac{-5+\sqrt[]{5}}{2},\ \frac{-5-\sqrt[]{5}}{2}$$  

• $$\frac{5+i\sqrt[]{95}}{12},\ \frac{5-i\sqrt[]{95}}{12}$$  

Multiple Choice

Solve using the quadratic equation.

$$2v^2+v-28=0$$  

• $$\frac{7}{2},\ -4$$  

• $$\frac{-1+\sqrt[]{57}}{4},\ \frac{-1-\sqrt[]{57}}{4}$$  

• $$-1+\sqrt[]{6},\ -1-\sqrt[]{6}$$  

• $$\frac{1+\sqrt[]{11}}{2},\ \frac{1-\sqrt[]{11}}{2}$$