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:
y = 3x+.5
Step-by-step explanation:
We know the y intercept (the value when x=0) is .5
We can find the slope from 2 points
(0,.5) and (1,3.5)
m = (y2-y1)/ (x2-x1)
= (3.5-.5)/(1-0)
= 3/1
= 3
We can use y = mx+b since we know the slope and the y intercept
y = 3x+.5
Answer:
Violet used 4 scoops of sugar and mixed it with 26 cups of lemonade and if it makes 234 cups of lemonade then there is 208. 26 scoops of sugar would violate the cups of lemonade.
Step-by-step explanation:
Answer:
y = -x - 1
Step-by-step explanation:
soo since we already know the slope we can subsitute it to the slope form equation
y = mx + b
y = -x + b
now to find the y intercept we have to subsitute the given point
-3 = -(2) + b
-3 = -2 + b
b = -1
Answer:
1st graph
Step-by-step explanation:
