Answer:
It's rational because it's not a decimal numbet
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)!!!
Sounds like you're asked to find
such that
In other words, find
that satisfies
We can factorize this as
In order that
describes a probability distribution, require that
for all
, which means we can ignore the possibility of
.
Let
.
Multiply both sides by
.
We want to find
that removes the quartic and quadratic terms from the equation, i.e.
so the cubic above transforms to
Substitute
and we get
![\implies y=\sqrt[3]{\dfrac{9+\sqrt{93}}{18}}](https://tex.z-dn.net/?f=%5Cimplies%20y%3D%5Csqrt%5B3%5D%7B%5Cdfrac%7B9%2B%5Csqrt%7B93%7D%7D%7B18%7D%7D)
![\implies a=\sqrt[3]{\dfrac{9+\sqrt{93}}{18}}-\dfrac13\sqrt[3]{\dfrac{18}{9+\sqrt{93}}}](https://tex.z-dn.net/?f=%5Cimplies%20a%3D%5Csqrt%5B3%5D%7B%5Cdfrac%7B9%2B%5Csqrt%7B93%7D%7D%7B18%7D%7D-%5Cdfrac13%5Csqrt%5B3%5D%7B%5Cdfrac%7B18%7D%7B9%2B%5Csqrt%7B93%7D%7D%7D)
The answer is 28 . I hope this helps
You can tell if a graph is a function by the x and y value if you find the x and y values, the x cannot repeat for the graph to be a function.
