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olga nikolaevna [1]
2 years ago
9

Which of the following equations have complex roots?

Mathematics
1 answer:
mestny [16]2 years ago
6 0

Answer:

A

Step-by-step explanation:

Complex roots of quadratic functions occur when the <u>discriminant is negative</u>.

<u>Discriminant</u>

b^2-4ac\quad\textsf{when}\:\:ax^2+bx+c=0

Evaluate the discriminant of each of the given equations.

\textsf{A.} \quad 3x^2+2=0

\implies a=3, \quad b=0, \quad c=2

\implies b^2-4ac=0^2-4(3)(2)=-24

As -24 < 0 the equation will have complex roots.

\textsf{B.} \quad 2x^2+1=7x

\implies 2x^2-7x+1=0

\implies a=2, \quad b=-7, \quad c=1

\implies b^2-4ac= (-7)^2-4(2)(1)=41

As 41 > 0 the equation does not have complex roots.

\textsf{C.} \quad 3x^2-1=6x

\implies 3x^2-6x-1=0

\implies a=3, \quad b=-6, \quad c=-1

\implies b^2-4ac=(-6)^2-4(3)(-1)=48

As 48 > 0 the equation does not have complex roots.

\textsf{D.} \quad 2x^2-1=5x

\implies 2x^2-5x-1=0

\implies a=2, \quad b=-5, \quad c=-1

\implies b^2-4ac=(-5)^2-4(2)(-1)=33

As 33 > 0 the equation does not have complex roots.

Learn more about discriminants here:

brainly.com/question/27444516

brainly.com/question/27869538

Learn more about complex roots here:

brainly.com/question/26344541

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