On these, we want to solve for x when f(x) = 0
1.
0 = x2 - 4x + 5
We can solve this for x using the quadratic formula with
a = 1, b = -4, and c = 5
\(x = {-b \pm \sqrt{b^2-4ac} \over 2a} \\~\\ x = {-(-4) \pm \sqrt{(-4)^2-4(1)(5)} \over 2(1)} ={4 \pm \sqrt{16-20} \over 2} ={4\pm\sqrt{-4}\over2} =\frac{4\pm2i}{2} \\~\\ x=2\pm i\)
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2.
0 = x2 + 3x + 4
We can solve this for x using the quadratic formula with
a = 1, b = 3, and c = 4
Can you finish this one from here?
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3.
0 = -x2 + 2x - 3
We can solve this for x using the quadratic formula with
a = -1, b = 2, and c = -3
\(x = {-2 \pm \sqrt{2^2-4(-1)(-3)} \over 2(-1)} = {-2 \pm \sqrt{4-12} \over -2} = {-2 \pm \sqrt{-8} \over -2} = \frac{-2\pm2i\sqrt2}{-2} \\~\\ x=1\pm i\sqrt2\)
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4.
0 = -x2 - 5x - 9
We can solve this for x using the quadratic formula with
a = -1, b = -5, and c = -9
Can you finish this one from here?
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5.
0 = 3x2 - x + 2
We can solve this for x using the quadratic formula with
a = 3, b = -1, and c = 2
\(x = {-(-1) \pm \sqrt{(-1)^2-4(3)(2)} \over 2(3)} ={1 \pm \sqrt{-23} \over 6} \\~\\ x={1 \pm i\sqrt{23} \over 6}\)
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