Answer:
A: This polynomial has a degree of 2 , so the equation 12x2+5x−2=0 has two or fewer roots.
B: The quadratic equation 12x2+5x−2=0 has two real solutions, x=−2/3 or x=1/4 , and therefore has two real roots.
Step-by-step explanation:
f(x) = 12x^2 + 5x - 2.
Since this is a quadratic equation, or a polynomial of second degree, one can easily conclude that this equation will have at most 2 roots. At most 2 roots mean that the function can have either 2 roots at maximum or less than 2 roots. Therefore, in the A category, 2nd option is the correct answer (This polynomial has a degree of 2 , so the equation 12x^2 + 5x − 2 = 0 has two or fewer roots).
To find the roots of f(x), set f(x) = 0. Therefore:
12x^2 + 5x - 2 = 0. Solving the question using the mid term breaking method shows that 12*2=24. The factors of 24 whose difference is 5 are 8 and 3. Therefore:
12x^2 + 8x - 3x - 2 = 0.
4x(3x + 2) -1(3x+2) = 0.
(4x-1)(3x+2) = 0.
4x-1 = 0 or 3x+2 = 0.
x = 1/4 or x = -2/3.
It can be seen that f(x) has two distinct real roots. Therefore, in the B category, 1st Option is the correct answer (The quadratic equation 12x2+5x−2=0 has two real solutions, x=−2/3 or x=1/4 , and therefore has two real roots)!!!
Answer its 20
Step-by-step explanation:
Answer:
The provided study is an experiment.
Step-by-step explanation:
Consider the provided information.
Observational study: In this study observer only observe the subjects, and measure variables of interest without allocating treatments to subjects.
For example: you want to examine the side effect of smoke on lung.
Experiment study:The researchers are applying treatments to experimental units in the research, then the effect of the treatments on the experimental units is observed.
For example: Flipping a coin
Now consider the provided information:
Thirty university students are divided into two groups. One group receives free tutoring in mathematics comma the other doesn't. After one semester comma scores on final mathematical examinations are compared.
Here, the researcher applying treatment to experimental units.
Thus, the provided study is an experiment.
Answer:
x = 23°
Step-by-step explanation:
- The figure given below is an irregular polygon with 7 sides
- The polygon is therefore an irregular heptagon.
We are required to determine the value of x
- We know the sum interior angles of a polygon is given by;
- Sum of interior angles = (n-2) 180 , where n is the number of sides
Therefore, in this case;
Sum of interior angles = (7 - 2 ) 180
= 900°
Hence;
7x° + 2x° + 8x° + 60° + 10x° + 8x° + 35° = 900°
35x° + 95° = 900°
35x° = 805°
x = 23°
Thus, the value of x is 23°
