The answer is 3 and -8.
To calculate this we will use the qudratic equation for ax² + bx + c = 0:
[tex]x= \frac{-b+/- \sqrt{ b^{2}-4ac } }{2a} [/tex]
In our equation x² + 5x - 24 = 0, we have:
a = 1
b = 5
c = -24
Now, let's implement that in the quadratic formula:
[tex]x= \frac{-5+/- \sqrt{ 5^{2}-4*1*(-24) } }{2*1} = \frac{-5+/- \sqrt{ 25+96} }{2} = \frac{-5+/- \sqrt{121} }{2} = \frac{-5+/-11}{2} [/tex]
From here, we have two solutions:
1. [tex] \frac{-5+11}{2} = \frac{6}{2}=3 [/tex]
2. [tex] \frac{-5-11}{2}= \frac{-16}{2} =-8 [/tex]
