f(0) = -14 is easy to
calculate. You can actually note that other than -14, every coefficient are
positive, so f will be increasing for x > 0 and it will eventually hit zero,
turn positive, and continue on getting larger. So it has exactly 1 positive
real root.<span> So this means that it only has exactly 1 positive real root
and these would be the possible numbers o</span>f positive real,
negative real, and complex zeros of f(x) = 4x3 + x2 + 10x – 14.
Positive Real: 1.
Negative Real: 2 or 0.
<span>Complex: 2 or 0 </span><span>
</span>The correct answer between all the choices given
is the second choice or letter B. I am hoping that this answer has satisfied
your query and it will be able to help you in your endeavor, and if you would
like, feel free to ask another question.
Answer:
m = -22
Step-by-step explanation:
Formula for parabola in it's vertex form is given by;
y = a(x - h)² + k
Where (h, k) is the coordinate of the vertex.
We are told that vertex is at (-6, 6) and the roots are at 10 and m.
Thus;
y = a(x - (-6))² + 6
y = a(x + 6)² + 6
Since 10 is a root, thus;
0 = a(10 + 6)² + 6
-6 = 256a
a = -6/256
a = -3/128
Thus,the equation is;
y = (-3/128)(x + 6)² + 6
Since m is a root, then;
0 = (-3/128)(m + 6)² + 6
-6 = (-3/128)(m + 6)²
Rearranging, we have;
128 × 6/3 = (m + 6)²
256 = m² + 12m + 36
m² + 12m - 256 + 36 = 0
m² + 12m - 220 = 0
Using quadratic formula, we have;
m = 10 or -22
We simplify through bxc^2;
We obtain bc^2;