question 1 (5 points)
if $p = 3x^2 - x + 2$ and $q = x^2 + 5x - 6$, then $p + q =$
a) $4x^2 - 4x - 4$
b) $4x^2 + 4x + 4$
c) $4x^2 - 4x + 4$
d) $4x^2 + 4x - 4$

question 2 (5 points)
use the quadratic formula to find the complex solutions to the equation $10x^2 - x + 9 = 0$.
a) $x = \frac{-1 \pm \sqrt{359}i}{20}$
b) $x = \frac{-1 \pm \sqrt{359}}{20}$
c) $x = \frac{1 \pm \sqrt{359}i}{2}$
d) $x = \frac{1 \pm \sqrt{359}i}{20}$

Question

question 1 (5 points)
if $p = 3x^2 - x + 2$ and $q = x^2 + 5x - 6$, then $p + q =$
a) $4x^2 - 4x - 4$
b) $4x^2 + 4x + 4$
c) $4x^2 - 4x + 4$
d) $4x^2 + 4x - 4$

question 2 (5 points)
use the quadratic formula to find the complex solutions to the equation $10x^2 - x + 9 = 0$.
a) $x = \frac{-1 \pm \sqrt{359}i}{20}$
b) $x = \frac{-1 \pm \sqrt{359}}{20}$
c) $x = \frac{1 \pm \sqrt{359}i}{2}$
d) $x = \frac{1 \pm \sqrt{359}i}{20}$

Accepted Answer

{ "quality": "clear", "question_count": 2, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Simplifying Algebraic Expressions", "Quadratic Formula", "Complex Quadratic Solutions" ], "new_concepts": [], "current_concepts": [ "Simplifying Algebraic Expressions", "Quadratic Formula", "Complex Quadratic Solutions" ] } ## Combine the polynomial expressions Using the *Simplifying Algebraic Expressions* knowledge point $$ \begin{aligned} P + Q &= (3x^2 - x + 2) + (x^2 + 5x - 6) \ &= (3x^2 + x^2) + (-x + 5x) + (2 - 6) \ &= 4x^2 + 4x - 4 \end{aligned} $$ ## Identify quadratic coefficients Using the *Quadratic Formula* and *Complex Quadratic Solutions* knowledge points $$ \begin{aligned} &10x^2 - x + 9 = 0 \ &a = 10, \quad b = -1, \quad c = 9 \end{aligned} $$ ## Apply the quadratic formula Using the *Quadratic Formula* and *Complex Quadratic Solutions* knowledge points $$ \begin{aligned} x &= \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \ x &= \frac{-(-1) \pm \sqrt{(-1)^2 - 4(10)(9)}}{2(10)} \ x &= \frac{1 \pm \sqrt{1 - 360}}{20} \ x &= \frac{1 \pm \sqrt{-359}}{20} \ x &= \frac{1 \pm \sqrt{359}i}{20} \end{aligned} $$ ## Question 1 (A) $4x^2 - 4x - 4$

(B) $4x^2 + 4x + 4$

(C) $4x^2 - 4x + 4$

(D) $4x^2 + 4x - 4$ ## Question 2 (A) $x = \frac{-1 \pm \sqrt{359}i}{20}$

(B) $x = \frac{-1 \pm \sqrt{359}}{20}$

(C) $x = \frac{1 \pm \sqrt{359}i}{2}$

(D) $x = \frac{1 \pm \sqrt{359}i}{20}$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Complex Quadratic Solutions" ] }

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QUESTION IMAGE

Question

Explanation:

Combine the polynomial expressions

Identify quadratic coefficients

Apply the quadratic formula

Answer:

Question 1

Question 2