sayan640 wrote:
KarishmaB MartyMurray , After solving -2*k + root over ( 4 - 5*k ) I am getting the range as -4 <k <1/4 and selected option A . What mistake did I make ? Can you please help ?
I found ( k+4 ) * (4k -1 ) < 0 and then used the wavy line method to get suitable range. Please help.
Notice that when you start off, you do not actually have this:
\( -2k + \sqrt{4 - 15k} = 0\)
What you actually have is this:
\( -2k + \sqrt{4 - 15k} > 0\)
Then, this:
\( \sqrt{4 - 15k} > 2k \)
So, when you take this step, you are squaring an inequality, which may not be a valid operation if the two sides can have different signs:
\( (\sqrt{4 - 15k})^2 > (2k)^2 \)
In fact, we can confirm that something is wrong with the approach of squaring both sides and using the wavy line method by noticing that, for any negative k with a large absolute value, \( -2k + \sqrt{4 - 15k}\) must clearly be positive.
So, you could either use a different approach, such as plugging in values, or use the approach you used and then check the values you get to adjust your result as needed to adjust for whatever might go wrong as a result of squaring the inequality.
I personally find that the easiest way to solve the problem is to see that any negative k with a large absolute value must work. So, A, B, and E are out because they restrict k to above -4 or above 0. Then, notice that any large positive k won't work. So, D is out. Thus, the only possible correct answer is C.