Answer:
Inequalities are,
y ≥ 4x + 2
y ≥ 2
Step-by-step explanation:
Solid yellow line of the graph attached passes through two points (0, -2) and (1, 2).
Let the equation of this line is,
y = mx + b
Slope of the line =
m =
m = 4
Y-intercept 'b' = -2
Equation of the line will be,
y = 4x - 2
Since shaded area is on the left side of this solid line so the inequality representing this region will be,
y ≥ 4x - 2
Another line is a solid blue line parallel to the x-axis.
Shaded region (blue) above the line will be represented by,
y ≥ 2
Therefore, the common shaded area of these inequalities will be the solution of the given inequalities.
For this case we have the following equation:
Let
We have:
By definition, given an equation of the form
The quadratic formula, to find the solution can be written as:
In this case we have:
Substituting in the quadratic formula we have:
See attached image
Answer:
Option B
The three roots of x^3 + 7x^2 + 12x = 0 is 0,-3 and -4
<u>Solution:</u>
We have been given a cubic polynomial.
We need to find the three roots of the given polynomial.
Since it is a cubic polynomial, we can start by taking ‘x’ common from the equation.
This gives us:
----- eqn 1
So, from the above eq1 we can find the first root of the polynomial, which will be:
x = 0
Now, we need to find the remaining two roots which are taken from the remaining part of the equation which is:
we have to use the quadratic equation to solve this polynomial. The quadratic formula is:
Now, a = 1, b = 7 and c = 12
By substituting the values of a,b and c in the quadratic equation we get;
<em><u>Therefore, the two roots are:</u></em>
And,
Hence, the three roots of the given cubic polynomial is 0, -3 and -4