Answer:
x=-6
Step-by-step explanation:
See the steps below:)
First solve the quadratic as you would an equation, so you will get two real zeroes p and q so that (x-p)(x-q)=0 is another way of expressing the quadratic. All quadratics can be represented graphically by a parabola, which could be inverted. When the x² coefficient is negative it’s inverted. If the coefficient of x² isn’t 1 or -1 divide the whole quadratic by the coefficient so that it takes the form x²+ax+b, where a and b are real fractions. The curve between the zeroes will be totally below the x axis for an upright parabola, and totally above for an inverted parabola. This fact is used for inequalities. An inequality will be <, ≤, > or ≥. This makes it easy to solve the inequality. If the position of the curve between the zeroes is below the axis then outside this interval it will be above, and vice versa. So we’ve defined three zones. x
q, and p
So firstly, we are going to complete the square for each polynomial. To do this, we need to split the middle term of each polynomial into two terms that add up to the middle term and multiply to the product of the first and third term.
Starting with 3x^2+26x+16, the two terms that fit are 24x and 2x since they add up to 26x and multiply to 48x^2. Now replace 26x with 24x + 2x:
Next, you are going to factor 3x^2 + 24x and 2x + 16 separately. Make sure they have the same quantity in the parentheses:
Next, thanks to distributive property, we can rewrite this as (3x + 2)(x + 8).
The process is going to be the same with the other 3 polynomials, so I'll brush through them real quickly:
So right now, just for reminder our fraction looks like this:
Next, cancel out (x+5), (x-3), and (3x+2) and your answer will be:
10÷2=5 5×2=10 10+20=30 30-5=25.