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In this lesson, we will learn how to solve quadratic equations whose roots are complex numbers.

Q1:

Determine the solution set of π₯ β 8 π₯ + 1 8 5 = 0 2 over the set of complex numbers.

Q2:

Which of the following best describes the roots of the equation π₯ + 1 7 = 0 2 ?

Q3:

Factor π₯ + π¦ 2 2 over the complex numbers.

Q4:

Solve the equation 5 π₯ + 1 = β 3 1 9 2 .

Q5:

Given that ( 8 β 6 π ) is one of the roots of π₯ + π π₯ + 6 = 0 2 , determine the value of π .

Q6:

Find the roots of the quadratic equation ( π₯ + 4 ) + 8 = 0 2 .

Q7:

Solve the equation 2 π₯ + 8 = 0 2 over the set of complex numbers.

Q8:

Find the solution set of π₯ + 5 = 0 2 .

Q9:

Find the solution set of π₯ + 8 π₯ + 1 8 5 = 0 2 given π₯ β β .

Q10:

Find the solution set of β 6 π₯ + 5 π₯ β 5 = 0 2 over β .

Q11:

Find the solution set of β π₯ + 1 6 = 0 4 in the set of complex numbers.

Q12:

Find the solution set of the equation π₯ + 3 = 0 2 in β .

Q13:

If the discriminant of a quadratic equation with real coefficients is negative, will its roots be a complex conjugate pair?

Q14:

Which of the following best describes the roots of the equation π₯ β 1 7 = 0 2 ?

Q15:

Factor π₯ + 9 2 over the complex numbers.

Q16:

Solve the equation π₯ = β 1 2 .

Q17:

Which quadratic equation has roots π₯ = Β± 3 π ?

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