Math helpppp so hard

Test Preparation SAT Preparation
1

<p>(x - 8)(x - k) = x^2 - 5kx + m</p>

<p>In the equation above, k and m are constants. If the equation is true for all values of x, what is the value of m?</p>

<p>a. 8
b. 16
c. 24
d. 32
e. 40</p>

<p>p. 527 #8</p>

<p>Level of difficulty: FIVEEEEE :( i suck at math k</p>

2

<p>x^2-kx-8x+8k-x^2+5kx-m=0 (since LHS=RHS, we subtract the RHS on both sides)</p>

<p>This simplifies into: 4kx-8x+8k-m=0</p>

<p>Set x=0. Now, 8k=m. So, k=m/8</p>

<p>Substitute into step 2. You will get mx/2-8x=0</p>

<p>Divide LHS and RHS by x.</p>

<p>You will get m/2-8=0</p>

<p>Therefore, m=16 (B)</p>

3

<p>Every single math question in the Blue Book that you could possibly have trouble with has been previously discussed in this forum. You will almost never have to make a new thread for a blue book math question, unless you aren’t satisfied with the answer given in the previous threads… please use google</p>

<p><a href=“http://talk.collegeconfidential.com/sat-preparation/759503-2-math-problems-stumped-usual-800er.html[/url]”>http://talk.collegeconfidential.com/sat-preparation/759503-2-math-problems-stumped-usual-800er.html&lt;/a&gt;&lt;/p&gt;

4

<p>You can plug in 2 numbers, which, for this case, are quite obvious choices: 8 and 0 for x.
When x = 8, the simplified equation reads 0 = 64 - 40k + m
When x = 0, the simplified equation reads 8k = m
Notice 8k = m can replace the ‘m’ in the first equation listed with an 8k, giving us an easily solvable equation which gives us k = 2.
Using the knowledge that k = 2, we can again use the first equation (without replacing ‘m’ immediately this time with 8k) and do 64 - 40(2), which gives us -16.
0 = -16 + m, m = 16.</p>

5

<p>Since no one has given the quickest way to solve this question in this thread I will add it here. </p>

<p>In the quadratic equation ax^2+bx+c, c is the product of the roots and b is the negative of the sum of the roots. In this problem the roots are 8 and k. So 8+k=5k from which it follows that 4k=8 and thus k=2. Also, 8k=m, from which it now follows that m=16.</p>

6

<p>I agree with Johnny. The magic of the search engine can definitely help you with your problems. I also don’t see a need for all of those extra letters.</p>

7

<p>YUP THANKS somebody already told me the that first timeeeeeee. I don’t see a need for a second opinion :)</p>