If

represent a family of surfaces for different values of the constant

. The gradient of the function

defined as

is a vector normal to the surface

.
Given <span>the paraboloid

.
We can rewrite it as a scalar value function f as follows:

The normal to the </span><span>paraboloid at any point is given by:

Also, the normal to the given plane

is given by:

Equating the two normal vectors, we have:
</span>

Since, -1 = 2 is not possible, therefore
there exist no such point <span>
on the paraboloid
such that the tangent plane is parallel to the plane 3x + 2y + 7z = 2</span>
.
There are two negative roots to the provided polynomial function
f(x) = x⁷ – 2x⁴ + 7x² + 2x – 2
<h3>What is polynomial?</h3>
Polynomial is the combination of variables and constants systematically with "n" number of power in ascending or descending order.

We have a polynomial function:
f(x) = x⁷ – 2x⁴ + 7x² + 2x – 2

Using the zero product property:

After solving:
x = -1, x = -0.853, and x = 0.418 (using the graph method)
Thus, there are two negative roots to the provided polynomial function
f(x) = x⁷ – 2x⁴ + 7x² + 2x – 2
Learn more about Polynomial here:
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Answer:
message me and i will tell u
Step-by-step explanation:
3√24= 3√2^2*6 = 3*2√6 = 6√6
2√384= 2√8^2*6 = 2*8√6 = 16√6
√96= √4^2*6 = 4√6
6√6 -16√6- 4√6 = -14√6
Final answer: -14√6
Answer:
nm/100
Step-by-step explanation: