Ineed the graph of a polynomial function of degree 10 has 5 x-intercepts, 4 of which have multiplicity 1 and one which has multiplicity 2. describe the nature and number of all the function's zeros. a) the function has 6 real zeros. b) the function has 4 imaginary zeros. c) the function has 6 real and 4 imaginary zeros. d) the function has 5 real and 5 imaginary zeros.

You're told there is a 10th degree polynomial. There are four roots of multiplicity 1 and one of multiplicity 2 (a double root).

Anytime there is a root of multiplicity 1 of a polynomial, its graph crosses the x-axis at that root. Anytime there is one of multiplicity 2, it means that we count the root twice and the graph has a tangency point.

The degree of a polynomial tells you how how many roots it has. Ours is degree 10, so it has ten roots. We have the four roots of multiplicity 1 and the one of multiplicity two, for a total of 6. (four and two).

So there are six real roots.

The rest of the roots are imaginary and non-real, and 10 - 6 = 4.  So there are four imaginary roots.

Thus choice C is best.

add 5 subtract 1

step-by-step explanation:

x = ±sqrt(10)

step-by-step explanation:

5 - 2x² = -15

subtract 5 from each side

5-5 - 2x² = -15-5

-2x^2   = -20

divide by -2 on each side

-2x^2   /-2= -20/-2

x^2 =10

take the square root on each side

sqrt(x^2 )=±sqrt(10)

x = ±sqrt(10)

check:

5 - 2x² = -15

+sqrt(10)

5 - 2(sqrt(10))² = -15

5 -2(10) = -15

5 -20 = -15

-15 = -15

-sqrt(10)

5 - 2(-sqrt(10))² = -15

5 -2(10) = -15

5 -20 = -15

-15 = -15