dilz27
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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]

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