Answer:
A
Step-by-step explanation:
Complex roots of quadratic functions occur when the discriminant is negative.
Discriminant
[tex]b^2-4ac\quad\textsf{when}\:\:ax^2+bx+c=0[/tex]
Evaluate the discriminant of each of the given equations.
[tex]\textsf{A.} \quad 3x^2+2=0[/tex]
[tex]\implies a=3, \quad b=0, \quad c=2[/tex]
[tex]\implies b^2-4ac=0^2-4(3)(2)=-24[/tex]
As -24 < 0 the equation will have complex roots.
[tex]\textsf{B.} \quad 2x^2+1=7x[/tex]
[tex]\implies 2x^2-7x+1=0[/tex]
[tex]\implies a=2, \quad b=-7, \quad c=1[/tex]
[tex]\implies b^2-4ac= (-7)^2-4(2)(1)=41[/tex]
As 41 > 0 the equation does not have complex roots.
[tex]\textsf{C.} \quad 3x^2-1=6x[/tex]
[tex]\implies 3x^2-6x-1=0[/tex]
[tex]\implies a=3, \quad b=-6, \quad c=-1[/tex]
[tex]\implies b^2-4ac=(-6)^2-4(3)(-1)=48[/tex]
As 48 > 0 the equation does not have complex roots.
[tex]\textsf{D.} \quad 2x^2-1=5x[/tex]
[tex]\implies 2x^2-5x-1=0[/tex]
[tex]\implies a=2, \quad b=-5, \quad c=-1[/tex]
[tex]\implies b^2-4ac=(-5)^2-4(2)(-1)=33[/tex]
As 33 > 0 the equation does not have complex roots.
Learn more about discriminants here:
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Learn more about complex roots here:
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