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:
x=51
Step-by-step explanation:
There are two ways you can go about this
You can either say that the sum of interior angles in a triangle is equal to 180 so you do 180-39-90=51
Or you could use the exterior angle theorem, which means that 90=39+x, simplify that and you get that x=51
Answer:
b ≈ 48.6°
Step-by-step explanation:
Using the sine ratio in the right triangle
sin b = 
= 
, then
b = 
( ) ≈ 48.6° ( to 1 dec. place )
Answer:
-68 is not a term in the given sequence
Step-by-step explanation:
The given sequence is -12, -17, -22, -27...
There is a common difference of d=-17--12=-5
The explicit rule for this sequence is 
Or 
To find the term that has a value of -68 we equate the explicit formula and solve for n.
The position should be a natural number.
Since n is a decimal, it tells us that -68 is not a term in the given sequence
The slope is 2/5
Use these coordinates
(-3,0) & (12,6)
