Consider the equation 3𝑥 + 𝑥2 = −7.
What does the value of the discriminant tell us about number of solutions to this equation?
Solve the equation. Does the number of solutions match the information provided by the discriminant? Explain.
Compute the value of the discriminant of the quadratic equation in each part. Use the value of the discriminant to predict the number and type of solutions. Find all real and complex solutions.
a. 𝑥2 + 2𝑥 + 1 = 0.
b. 𝑥2 + 4 = 0
c. 9𝑥2 − 4𝑥 − 14 = 0
d. 3𝑥2 + 4𝑥 + 2 = 0
e. 𝑥 = 2𝑥2 + 5
f. 8𝑥2 +4𝑥 + 32 = 0
If 𝑏2 − 4𝑎𝑐 > 0, there are two real solutions to 𝑎𝑥2 + 𝑏𝑥 + 𝑐 = 0.
If 𝑏2 − 4𝑎𝑐 = 0, there is one real solution to 𝑎𝑥2 + 𝑏𝑥 + 𝑐 = 0.
If 𝑏2 − 4𝑎𝑐 < 0, there are two complex solutions to 𝑎𝑥2 + 𝑏𝑥 + 𝑐 = 0.
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