Solve −3x2 − 4x − 4 = 0
2 answers:
This is a quadratic formula with a general form of a²x + bx + c = 0. For quadratic equations, we can solve for its two roots using the quadratic formula shown in the attached picture.
a = -3
b = -4
c = -4
x = [-(-4) + √(-4)² - 4(-3)(-4)]/2(-3) = <em>2 + √-32/2</em>
x = [-(-4) - √(-4)² - 4(-3)(-4)]/2(-3) =<em> 2 - √-32/2</em>
a = -3
b = -4
c = -4
x = [-(-4) + √(-4)² - 4(-3)(-4)]/2(-3) = <em>2 + √-32/2</em>
x = [-(-4) - √(-4)² - 4(-3)(-4)]/2(-3) =<em> 2 - √-32/2</em>
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The range of the equation is
Explanation:
The given equation is
We need to determine the range of the equation.
<u>Range:</u>
The range of the function is the set of all dependent y - values for which the function is well defined.
Let us simplify the equation.
Thus, we have;
This can be written as
Now, we shall determine the range.
Let us interchange the variables x and y.
Thus, we have;
Solving for y, we get;
Applying the log rule, if f(x) = g(x) then , then, we get;
Simplifying, we get;
Dividing both sides by , we have;
Subtracting 7 from both sides of the equation, we have;
Dividing both sides by 2, we get;
Let us find the positive values for logs.
Thus, we have,;
The function domain is
By combining the intervals, the range becomes
Hence, the range of the equation is