Barrons Question Help

Archive SAT Subject Test Preparation
1

<p>The Vertical distance between the min and max values of the finction y = abs((-rt2sinrt3)) is </p>

<p>a: 1.4.1
b 1.732
c 2.094
d 2.828
e 3.464</p>

<p>I tried to plot the equation but I just got a straight line</p>

<p>another one</p>

<p>a positive rational root of the equation 4x^3-x^2+16x-4 = 0 is:</p>

<p>a 1/4
2 1/2
3 3/4
d 1
e 2</p>

<p>I found the factors of the constant term and the leading coefficient but there is more than one postive rational root? Also according the descartes rule of signs there are either 3 or 1 roots</p>

2

<p>write the function properly please like - (sin (x^1/3))^1/3 etc</p>

3

<p>I cant write the root sign</p>

4

<p>write like x^(1/2)</p>

5

<p>sqrt(x) is usually most readable. If you know LaTeX, \sqrt{x} works as well.</p>

6

<p>Also for the second one, polynomial factors to (4x-1)(x^2 + 4) = 0. The only positive rational root is 1/4.</p>

<p>The rational root theorem only tells you that if P(x) has a rational root, it is of the form +/- p/q (lowest terms) where p divides the constant term and q divides the leading coefficient. You would have to check all possible roots.</p>

7

<p>3 roots , 2 irrational , 1 rational
rational - 1/4 irrational - .123 + 2iota and conjugate</p>

8

<p>@miter how did you factor that? </p>

<p>more importantly whats the fastest way to solve the problem?</p>

9

<p>in order to factorize cubic equations (by hand) - use hit/trial to find 1 factor say 1/4 so (x-1/4), then divide the whole equation by (x-1/4) and you will get a power 2 equation, use splitting of middle term or Determinant to solve for furthur 2 values of x.</p>

<p>or use a GDC…</p>

10

<p>use a GDC and get all factors - easiest way</p>

11

<p>I just looked at patterns in the coefficients and saw that 4x-1 is a factor. Then the polynomial can be written as (x^2)(4x-1) + 4(4x-1), and it factors as above.</p>

<p>What is GDC?</p>

12

<p>graphing display calc (graphing calc)</p>

13

<p>Well…you could just simply plug in the answer choices and see which one works. Easily done by defining a function on your graphing calculator.</p>

14

<p>or, press APPS on calc, press ENTER choose OPTION 1 , set variable power 3, fill in the coefficients, press GRAPH button , get all roots (real and imaginary)</p>

<p>APPS —> PlySmlt2—>ENTER----->1.----->Order - 3------>GRAPH------>coeffiecients-------> GRAPH------>answer</p>

15

<p>for question 1 , </p>

<p>Q: | -rt(2)*sin(rt(3)x) |
Ans - plot a graph. keep in mind that angle is in radian mode.</p>

<p>MODE------>Radians------>plot</p>