3. how is the fundamental theorem of algebra true for quadratic polynomials?

Step-by-step explanation:

Theorm-The Fundamental Theorem of Algebra: If P(x) is a polynomial of degree n ≥ 1, then P(x) = 0 has exactly n roots, including multiple and complex roots.

Let's verify that the Fundamental Theorem of Algebra holds for quadratic polynomials.

A quadratic polynomial is a second degree polynomial. According to the Fundamental Theorem of Algebra, the quadratic set = 0 has exactly two roots.

As we have seen, factoring a quadratic equation will result in one of three possible situations.

graph 1

The quadratic may have 2 distinct  real roots. This graph crosses the

x-axis in two locations. These  graphs may open upward  or downward.

graph 2

It may appear that the quadratic  has only one real root. But, it  actually has one repeated root.  This graph is tangent to the x-axis  in one location (touching once).

graph 3

The quadratic may have two  non-real complex roots called  a conjugate pair. This graph will  not cross or touch the x-axis, but  it will have two roots.

answer: city needs 2.4 inches of rainfall more to match the record of 40 inches.

step-by-step explanation:

since we have given that

total annual rainfall a city record = 40 inches

this year, total rainfall recorded = 37.6 inches

number of inches of rainfall   is needed to match the record of 40 inches is given by

hence, city needs 2.4 inches of rainfall more to match the record of 40 inches.

y = 5x + 17

step-by-step explanation:

a perpendicular line will be the opposite reciprocal slope of the given equation.   the slope given is -1/5 so the opposite reciprocal is 5

find b:

7 = 5 (-2) + b

7 = -10 + b

17 = b

write equation

y = 5x + 17