x2 + 3x - 18 < 0
A.(-6, 3)
B. (-3, 6)
c.(-∞, -6)∪(3, ∞)
D. (-∞, -3)∪(6, ∞)
Find two numbers that multiply to negative 18 and add to 3. (x+6)(x-3)
thankyou but, so what would you say the answer is a,b,c or d?
If you sketch the curve f(x) = x²+6x-18=0, it will be concave upwards, which means that if the curve cuts the x-axis, the domain of the function f(x)<0 will be between the two roots of f(x)=0. Thus c and d are not appropriate answers.
Jen already factorized f(x)=(x+6)(x-3).
You will need to find the value of the roots (where the curve cuts the x-axis) and find the appropriate response.
If you need help understanding the interval notation, please post.
To determine the solution set of the inequality x^2 + 3x - 18 < 0, we can use a method called factoring.
Here's how you can do it step by step:
Step 1: Factor the quadratic expression x^2 + 3x - 18.
To factor the quadratic expression, we need to find two numbers that multiply to give -18 and add up to 3. The numbers that satisfy these conditions are 6 and -3. Therefore, we can write x^2 + 3x - 18 as (x + 6)(x - 3).
Step 2: Set each factor equal to zero and solve for x.
Setting (x + 6) equal to zero, we get x + 6 = 0, which gives x = -6.
Setting (x - 3) equal to zero, we get x - 3 = 0, which gives x = 3.
Step 3: Create a sign chart.
We create a sign chart by plotting the critical points -6 and 3 on a number line.
Number line:
-∞ -6 3 ∞
Step 4: Test a value in each interval.
We can choose a test value in each interval and substitute it into the original inequality to determine whether the numbers in that interval satisfy the inequality or not.
For the interval (-∞, -6), we can choose x = -7. Substituting this value into the inequality, we get (-7)^2 + 3(-7) - 18 < 0, which is true. Therefore, this interval satisfies the inequality.
For the interval (-6, 3), we can choose x = 0. Substituting this value into the inequality, we get 0^2 + 3(0) - 18 < 0, which is false. Therefore, this interval does not satisfy the inequality.
For the interval (3, ∞), we can choose x = 4. Substituting this value into the inequality, we get 4^2 + 3(4) - 18 < 0, which is true. Therefore, this interval satisfies the inequality.
Step 5: Write the solution set.
From the sign chart and the test values, we can see that the inequality is satisfied for (-∞, -6) and (3, ∞). Therefore, the solution set is (-∞, -6)∪(3, ∞).
In conclusion, the correct answer is c. (-∞, -6)∪(3, ∞).