If the two roots of the quadratic \( 4x^2+7x+k\) are \( \frac{-7\pm i\sqrt{15}}{8}\), what is k?
+72
*Since I'm not sure if that "i" before the \(\sqrt{15}\) , I'm going to assume it's not there. If another user knows what to do with the "i" then you should follow their answer.*
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Given the quadratic formula: \(x = {-b \pm \sqrt{b^2-4ak} \over 2a}\) we already know what the variable a and b are 4 and 7, respectively.
Now, we plug in the knowns into the formula, and we get: \(x = {-7 \pm \sqrt{7^2-4(4)(k)} \over 2(4)}\)
As a result, you get: \(x = {-7 \pm \sqrt{49-16k} \over 8}\)
Now, since we know that the number inside the square root is 15, to solve for k you can do this:
49-16k = 15
-16k = 15-49
-16k = -34
k = -34 / -16
k = 2.125
Therefore, k equals to 2.125
