A polynomial function has a root of -5 with multiplicity 3, a root of 1 with multiplicity of 2, and a root of 3 with multiplicity 7. If the function has a negative leading coefficient and is of even degree which statement about the graph is true?

a) function is positive on (-∞,-5)
b) fuction is negative on (-5,3)
c) function is positive on (-∞,1)
d) function is negative on (3,∞)

  d)  function is negative on (3,∞)

Step-by-step explanation:

The even degree and negative leading coefficient tell you that the function is negative as x ⇒ ±∞. (Selections A and C cannot be correct.)

The odd multiplicity tells you the function crosses the x-axis at x=-5 and x=3, so will be non-negative between those values. (Selection B cannot be correct.)

The function is negative on (3, ∞).

a complex number is a number that can be expressed in the form a + bi, where a and b are real numbers, and i is a solution of the equation x2 = −1. because no real number satisfies this equation, i is called an imaginary number. has no real solution, since the square of a real number cannot be negative.