Provide an Appropriate Response $k , a , b$ , And $c$

question 386

Multiple Choice

Provide an appropriate response.
-Suppose that $k , a , b$ , and $c$ are real numbers and that the polynomial function $f$ may be expressed in factored form as $f ( x ) = ( x - k ) \left( a x ^ { 2 } + b x + c \right)$ . If $b ^ { 2 } - 4 a c = - 57$ , determine the number of real and imaginary zeros that $f$ has.

• A) 3 real zeros, 0 imaginary zeros
• B) 2 real zeros, 2 imaginary zeros
• C) 2 real zeros, 1 imaginary zero
• D) 1 real zero, 2 imaginary zeros

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Definitions:

Beta Particle

A fast-moving electron or positron with high energy released during the radioactive decay of an atomic nucleus.

Atomic Nucleus

The small, dense region at the center of an atom, consisting of protons and neutrons and containing nearly all the atom's mass.

Beta Particle

A high-energy, high-speed electron or positron emitted by the radioactive decay of an atomic nucleus during beta decay.

Atomic Nucleus

The dense central core of an atom, containing protons and neutrons, around which electrons orbit.