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=2 , y = 1
Step-by-step explanation:
x + 2(2x-3) = 4
x+4x-6=4
5x-6=4
5x= 10
x=10/5
x=2
subs x=2 into x +2y=4
2+2y=4
2y=2
y=2/2
y=1
Answer:
20% or 1/5 or 0.2
Step-by-step explanation:
1. There are 10 sections, which means <em>each section has a a chance of 10% to be landed on</em>.
2. There are <em>two multiples of four under 10: 4 and 8</em>.
That means there is a <em>2 * 10%</em> = 20% chance that the spinner will land on a multiple of 4.
We have 2xπxr = 14π;
Then, r = 7;
The area of the circle is πx(r^2) = 49π.
-4/-8 6/x
y=12
the answer is y=12 when x=6
