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Consider the equation x^2+8x+-4=0.

Without solving the quadratic explain how you know if the equation has real or imaginary solutions.

Sep 18, 2018

#1
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$$\text{For a quadratic equation }a x^2 + b x + c = 0 \\ \\ \text{a non-negative discriminant, i.e. }\\ D=b^2 - 4 a c \\ \text{indicates real roots}$$

$$\text{the discriminant in this case is } \\ D=64+16 = 80 > 0 \\ \text{and thus we have real roots}$$

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Sep 18, 2018
edited by Rom  Sep 18, 2018

#1
+5226
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$$\text{For a quadratic equation }a x^2 + b x + c = 0 \\ \\ \text{a non-negative discriminant, i.e. }\\ D=b^2 - 4 a c \\ \text{indicates real roots}$$
$$\text{the discriminant in this case is } \\ D=64+16 = 80 > 0 \\ \text{and thus we have real roots}$$