Question

Solve using the quadratic formula. Show all work. Write each solution in simplest form. No decimals.

Answer 1

Step-by-step explanation:

${x}^{2} + 3x - 5 = 0$

a =1. b = 3. c = -5

Quadratic equation

$x = \frac{ - b + \sqrt{ {b}^{2} - 4ac} }{2a} \\ = \frac{ - 3 \: + \sqrt{ {3}^{2} \: - 4(1)( - 5) } }{2} \\ = \frac{ - 3 \: + \: \sqrt{29} }{2}$

Note: the plus sign in the quadratic equation should read "+-"

Therefore, the roots of the quadratic equation are

$\frac{ - 3 \: + \: \sqrt{29} }{2} \: \: and \: \: \frac{ - 3 \: - \: \sqrt{29} }{2}$