<p>If the parabola given y= x^2-kx+4 has two real and distinct zeros then what are the possible values of k? </p>
<p>the answer is k<-4 or k>4</p>
<p>I know the discriminant says k>4 so i picked that one. </p>
<p>The solution says "the discriminant must be positive therefore k^2-16>0 which implies that x<4 or k>4. "</p>
<p>I'm not sure how it implies x<4....can some one explan the solution?This is from the 15 realistic tests.</p>
<p>because k is squared, once squared, the answer will always be positive. 5 squared is 25 as is -5 squared. this can be found if you substitute an = sign for the > and solve the equation. there are two solutions, 4 and -4 so they both must be incorporated in the answer. hope that helps!</p>
<p>First off, this book "15 realistic tests" is not exactly realistic. The questions are much harder and some are outside of the SAT II scope.
Second, there are typos in the book, and this is one of them (on page 235).
The answer should be k<-4 or k>4.</p>
<p>There are two points on the parabola y=x^2 where y=16: x=-4 and x=4.<br>
Branches of the parabola above the line y=16 are where
x<-4 or x>4.
That's why k^2>16 when k<-4 or k>4.
++++++++
chocaholic0029 is right, but algebraic solution is not as clear as graphic one.</p>
<p>By definition sq.root(k^2)=|k|.
If you take a sq.root of both sides of
k^2 > 16 you get
|k| > 4.
For k<0 it's -k>4 and
for k>=0 it's k>4.
The answer then is
k<-4 or k>4.
+++++++
Back to "15 realistic tests".
I would recommend using it only when you are done with the Spark Notes SAT II math books and maybe Barron's if you aim at 800. Unfortunately both have typos too. Plus, Barron's is an overkill, but not to a degree of
"15 ...tests".</p>
<p>thanks a lot.....i'm using PR & SparkNotes but i also have the 15......i guess i won't use it that much...</p>