Question

9/20

Find the number of real number solutions for the equation. x2 + 5x + 7 = 0
nd
01
ations
02
O cannot be determined
are
00
e
100%

Answer 1

For this case we must find the solution of the following quadratic equation:

`x ^ 2 + 5x + 7 = 0`

Where:

`a = 1\\b = 5\\c = 7`

Then, the solution is given by:

`x = \frac {-b \pm \sqrt {b ^ 2-4 (a) (c)}} {2a}`

Substituting the values:

`x = \frac {-5 \pm \sqrt {5 ^ 2-4 (1) (7)}} {2 (1)}\\x = \frac {-5 \pm \sqrt {25-28}} {2}\\x = \frac {-5 \pm \sqrt {-3}} {2}`

By definition we have:
`i ^ 2 = -1`

`x = \frac {-5 \pm \sqrt {3i ^ 2}} {2}\\x = \frac {-5 \pm i \sqrt {3}} {2}`

Thus, we have two complex roots.

Answer:

The equation has no real roots.