2x^2 + x + 3=0 has only complex roots.
The determinant is 1-4*2*3 = -23
-23 (or any determinant) is the part under the square root sign, If that determinant is negative, knowing you cannot take the square root of a negative number, we know the answers must be complex.
Answer:
y=-2x-7 D
Step-by-step explanation:
Part 1: The general form for this matches y^2 = -4cx, which implies that this opens to the left. (Imagine assigning any value of y, whether positive or negative, which would result in a positive left-hand value. Then to match this sign, the value of x must be negative so that the right-hand side becomes positive as well.)
Part 2: The distance from the vertex to the directrix is given by c. This equation has its vertex at the origin (0, 0). If it opens to the left, the directrix is a vertical line to the right of the origin. This equation is y^2 = -4(1/2)x, so c = 1/2, and the directrix has the equation x = 1/2.
Part 3: The focus is inside the parabola, but it is the same distance from the vertex as the directrix. This distance is 1/2 units, and it will be to the left of the vertex. So the focus is at (-1/2, 0).
Answer:
All options are correct.
Step-by-step explanation:
In option (A), the given equation is
Add 37 on both sides.
Subtract x from both sides.
LHS=RHS for all values of x. It means equation x-37=x-37 has infinite many solutions.
Similarly.
In option (B), the given equation is
LHS=RHS for all values of x. It means equation 73x-37=73x-37 has infinite many solutions.
In option (C), the given equation is
LHS=RHS for all values of x. It means equation 37x-37=37x-37 has infinite many solutions.
In option (D), the given equation is
LHS=RHS for all values of x. It means equation 74x-37=74x-37 has infinite many solutions.
Therefore, all options are correct.
