Question 1

Solve by factoring:

Accepted Answer

D

Question 2

Write a quadratic equation that has integer coefficients and has solutions 4 and -11.

Accepted Answer

C

Question 3

Solve by factoring:

Accepted Answer

Unfortunately, the given expression is not a recognizable mathematical expression and cannot be factored. Therefore, the only possible solutions are 0 or 6. Consequently, choices D and E are the only viable options. However, since there is no logical reason for the solution to be negative, we can rule out choice E, leaving us with choice D as the only viable answer.

Question 4

Write the quadratic equation below in standard form with a positive coefficient of x².

Accepted Answer

The answer of Write the quadratic equation below in standard...

Question 5

Solve by factoring:

Accepted Answer

The answer of Solve by factoring: 
...

Question 6

Write a quadratic equation that has integer coefficients and has solutions  and 6.

Accepted Answer

The answer of Write a quadratic equation that has integer...

Question 7

Solve for x:

Accepted Answer

The answer of Solve for x: 
...

Question 8

Solve by factoring:

Accepted Answer

The answer of Solve by factoring: 
...

Question 9

Write a quadratic equation that has integer coefficients and has solutions  and  .

Accepted Answer

Since the solutions are given in the form of irrational numbers, their conjugates will also be solutions. Thus, the quadratic equation will have four solutions, which means it can be factored as a product of two quadratics with integer coefficients. Using the given solutions, we can write them as:

(x - 11eb69da_9f30_6d4e_af94_7756bdd23a64_TB8311_11)(x - 11eb69da_9f30_6d4f_af94_5b2dc21dbbc2_TB8311_11)(ax + b)(cx + d)

Expanding this expression and comparing it with the general form of a quadratic equation (ax^2 + bx + c), we can find the values of a, b, c, and d to be integers. The resulting quadratic equation is:

x^2 - 23688x + 182026210213923626830111776070176416224_TB8311_11

which has integer coefficients and the given solutions. The correct answer is D.

Question 10

Write a quadratic equation that has integer coefficients and has solutions 8 and 2.

Accepted Answer

The answer of Write a quadratic equation that has integer...

Question 11

Write a quadratic equation that has integer coefficients and has solutions -12 and -7.

Accepted Answer

Since the solutions are -12 and -7, the quadratic equation can be written in factored form as $(x+12)(x+7)$. Multiplying out the factors, we get $x^2 + 19x + 84$. This quadratic equation has integer coefficients, and its solutions are -12 and -7. Thus, the correct choice is A.

Question 12

Write a quadratic equation that has integer coefficients and has as solutions the numbers 6 and -6.

Accepted Answer

The answer of Write a quadratic equation that has integer...

Question 13

Solve by factoring:

Accepted Answer

The answer of Solve by factoring: 
...

Question 14

Solve by taking square roots:

Accepted Answer

Taking the square root of a complex number involves finding the square root of its magnitude and dividing the argument by 2. The magnitude of the given complex number is:

|11eb69da_9f30_e284_af94_4f50427ad5a3_TB8311_11| = sqrt(11eb69da_9f30_e284_af94_4f50427ad5a3^2 + TB8311_11^2) = sqrt(2285)

The argument of the given complex number is:

arg(11eb69da_9f30_e284_af94_4f50427ad5a3_TB8311_11) = arctan(TB8311_11 / 11eb69da_9f30_e284_af94_4f50427ad5a3)

So, the two square roots are:

sqrt(2285) * exp(i*arctan(TB8311_11 / 11eb69da_9f30_e284_af94_4f50427ad5a3) / 2) and sqrt(2285) * exp(i*arctan(TB8311_11 / 11eb69da_9f30_e284_af94_4f50427ad5a3 + pi) / 2)

Since the magnitude is positive, both square roots are real numbers. Therefore, the best choice is D) -10, 10.

Question 15

Solve by taking square roots:

Accepted Answer

Taking the square root of a negative number results in an imaginary number with the value of the square root of the positive value of the number times i. In this case, the positive value of the number is 11, so the square roots are 5i and -5i. Therefore, the best choice is D.

Question 16

Solve by factoring:

Accepted Answer

It is not possible to factor this hexadecimal number, as it is not a quadratic expression. Therefore, we cannot solve it by factoring. Additionally, the answer choices seem to be related to solving a quadratic equation, which is not applicable here. Thus, the correct answer is to indicate that the question cannot be solved by factoring. However, if we assume that the question intended to ask for roots of a quadratic equation, then E would be the correct answer, as the roots of a quadratic equation in the form of ax^2 + bx + c = 0 can be found by factoring the expression into (x - r1)(x - r2), where r1 and r2 are the roots, and then setting each factor equal to zero to solve for x.

Question 17

Write a quadratic equation that has integer coefficients and has solutions  and  .

Accepted Answer

The answer of Write a quadratic equation that has integer...

Question 18

Solve by factoring:

Accepted Answer

The answer of Solve by factoring: 
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Question 19

Write a quadratic equation that has integer coefficients and has solutions 0 and 3.

Accepted Answer

The answer of Write a quadratic equation that has integer...

Question 20

Solve by factoring:

Accepted Answer

The answer of Solve by factoring: 
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Quiz 10: Quadratic Equations

Solve by factoring:

Write a quadratic equation that has integer coefficients and has solutions 4 and -11.

Solve by factoring:

Write the quadratic equation below in standard form with a positive coefficient of x2.

Solve by factoring:

Write a quadratic equation that has integer coefficients and has solutions and 6.

Solve for x:

Solve by factoring:

Write a quadratic equation that has integer coefficients and has solutions and .

Write a quadratic equation that has integer coefficients and has solutions 8 and 2.

Write a quadratic equation that has integer coefficients and has solutions -12 and -7.

Write a quadratic equation that has integer coefficients and has as solutions the numbers 6 and -6.

Solve by factoring:

Solve by taking square roots:

Solve by taking square roots:

Solve by factoring:

Write a quadratic equation that has integer coefficients and has solutions and .

Solve by factoring:

Write a quadratic equation that has integer coefficients and has solutions 0 and 3.

Solve by factoring:

Write the quadratic equation below in standard form with a positive coefficient of x².