Answer:
[tex]\sf c = -4[/tex] and [tex]\sf b = -6[/tex]
Explanation:
using the formula: [tex]\sf x = \frac{ -b \pm \sqrt{b^2 - 4ac}}{2a}[/tex]
Here the a = 1
using the equation:
[tex]3 \pm\sqrt{13}= \frac{ -b \pm \sqrt{b^2 - 4(1)c}}{2(1)}[/tex]
[tex]6 \pm2\sqrt{13}= -b \pm \sqrt{b^2 - 4(1)c}}[/tex]
matching the coefficients: b = - 6
find c:
[tex]6 \pm2\sqrt{13}= -(-6) \pm \sqrt{(-6)^2 - 4(1)c}}[/tex]
[tex]6 \pm2\sqrt{13}= 6 \pm \sqrt{36 - 4c}}[/tex]
[tex]\sf 6 \pm\sqrt{52}= 6 \pm \sqrt{36 - 4c}}[/tex]
[tex]\sf 36-4c = 52[/tex]
[tex]\sf -4c = 52-36[/tex]
[tex]\sf -4x = 16[/tex]
[tex]\sf c = -4[/tex]
