Since the value of the discriminant (-19) < 0, no real solution(s)/root(s) exist for the equation. Thus, we can choose the first option:
"Zero, because the discriminant is negative".
A quadratic equation is a polynomial of degree 2, in a single variable x.
The standard form of a quadratic equation is ax² + bx + c = 0.
The quadratic formula is used to find the solution(s)/root(s) of this equation.
The quadratic formula is:
[tex]x = \frac{-b \pm \sqrt{b^2 - 4ac} }{2a}[/tex]
In this formula, [tex]b^2-4ac[/tex] is called the discriminant (D).
The solution(s)/root(s) of the equation, depends on this discriminant value as follows:
- When D > 0, the roots of the equation are real and distinct.
- When D = 0, the roots of the equation are real and equal.
- When D < 0, then no real roots exist.
In the question, we are given that the simplest form of Quincy's equation in the radical form was,
[tex]x = \frac{-3 \pm \sqrt{-19} }{2}[/tex].
Comparing this to the quadratic formula,
[tex]x = \frac{-b \pm \sqrt{b^2 - 4ac} }{2a}[/tex]
we get the discriminant (D) = -19.
Since the value of the discriminant (-19) < 0, no real solution(s)/root(s) exist for the equation. Thus, we can choose the first option:
"Zero, because the discriminant is negative".
Learn more about discriminant at
https://brainly.com/question/14072293
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For complete question, refer to the attachment.
