use the discriminant to determine the number and nature of the solutions to the quadratic equation. do not solve the equation.

\4x^2 + \sqrt{11}x + 6 = 0\

the discriminant is equal to
(type an integer or a simplified fraction.)

the equation has
- two real solutions.
- exactly one real solution.
- two nonreal solutions.

Question

use the discriminant to determine the number and nature of the solutions to the quadratic equation. do not solve the equation.

\4x^2 + \sqrt{11}x + 6 = 0\

the discriminant is equal to
(type an integer or a simplified fraction.)

the equation has
- two real solutions.
- exactly one real solution.
- two nonreal solutions.

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Discriminant Analysis" ], "new_concepts": [], "current_concepts": [ "Discriminant Analysis", "Quadratic Equations" ] } ## Identify coefficients of the quadratic equation $$ \begin{aligned} &a = 4 \ &b = \sqrt{11} \ &c = 6 \end{aligned} $$ ## Calculate the discriminant $$ \begin{aligned} D &= b^2 - 4ac \ D &= (\sqrt{11})^2 - 4(4)(6) \ D &= 11 - 96 \ D &= -85 \end{aligned} $$ ## Determine the number and nature of solutions $$ \begin{aligned} &D = -85 < 0 \ &\text{Since } D < 0, \text{ the equation has two nonreal solutions.} \end{aligned} $$ Use the discriminant to determine the number and nature of the solutions to the quadratic equation. Do not solve the equation. $4x^2 + \sqrt{11}x + 6 = 0$ The discriminant is equal to -85 The equation has two nonreal solutions. { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Discriminant Analysis" ] }

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Identify coefficients of the quadratic equation

Calculate the discriminant

Determine the number and nature of solutions

Answer: