Question

9/20

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.