How Many Roots? Examples

Example 1
How many real number or complex number roots does the following equation have?

y = x ^{2} + 4x + 1

There's an easier way to find out than going through the trouble of finding all the roots yourself.

Let's use the discriminate! b^{2} – 4ac .

Er…we might need to know what a , b , and c are first.

a = 1b = 4c = 1

16 – 4(1)(1) = 16 – 4 = 12

The discriminate is positive, so there are two real number roots for this equation.

Show Next Step

Example 2
How many real number or complex number roots does the following equation have?

y = x ^{2} – x +3

Let's start off with the set up.

a = 1b = -1c = 3

And now we plug away.

b ^{2} – 4ac = (-1)^{2} – 4(1)(3) = 1 – 12 = -11

This time the discriminate is negative, so there are two complex number roots (and no real number roots).

Show Next Step

Example 3
How many real number or complex number roots does the following equation have?

y = -2x ^{2} – 4x + 1

a = -2b = -4c = 1

b ^{2} – 4ac = (-4)^{2} – 4(-2)(1) = 12 + 8 = 20

A positive outcome leads to real results—and two real roots.

Show Next Step

Example 4
How many real number or complex number roots does the following equation have?

y = -9x ^{2} + 6x – 1

a = -9b = 6c = -1

b ^{2} – 4ac = (6)^{2} – 4(-9)(-1) = 36 – 36 = 0

The discriminate…it's nothing. A nihilist's dream. In the end, there is only one (real root).

Show Next Step

People who Shmooped this also Shmooped...