How many real-number solutions does the equation have?
0 equals 2 x squared minus 20 x plus 50
A. two solutions
B. one solution
C. no solutions
D. infinitely many solutions
C. no solutions
Graph the set of points. Which model is most appropriate for the set?
(negative 6, 0), (negative 4, 2), (negative 3, 3), (2, 8)
A. a coordinate plane with points plotted that form a linear graph with positive slope; points are located in the first, second, and third quadrants.
B. a coordinate plane with points plotted that form a quadratic graph; points are located in the first, second, and third quadrants.
C. a coordinate plane with points plotted that form a quadratic graph; points are located in the first, fourth, and third quadrants.
D. a coordinate plane with points plotted that form a linear graph with positive slope; points are located in the first, fourth, and third quadrants.
D. a coordinate plane with points plotted that form a linear graph with positive slope; points are located in the first, fourth, and third quadrants.
What type of equation will best fit the data below?
A scatter plot is shown. The points are in the shape of an upside down upper case U.
A. quadratic
B. linear
C. exponential
A. quadratic
To determine the number of real-number solutions for the equation 0 = 2x^2 - 20x + 50, we can use the discriminant formula from quadratic equations. The discriminant (denoted as Δ) is given by the expression b^2 - 4ac, where a, b, and c are coefficients of the quadratic equation ax^2 + bx + c = 0.
In this case, the equation is 2x^2 - 20x + 50 = 0, so:
- a = 2
- b = -20
- c = 50
Now, let's substitute the values into the discriminant formula:
Δ = (-20)^2 - 4 * 2 * 50
= 400 - 400
= 0
The discriminant Δ is equal to 0. When the discriminant is equal to zero, it means that the quadratic equation has exactly one real solution. Therefore, the answer is:
B. One solution