SOLVE x^4 − 15x^2 − 16 = 0
What are the roots of the equation?

roots : 4, -4, i, -i

Step-by-step explanation:

This gets a bit tricky.

We have to substitude x^2 as u in this problem.

Now to rewrite x^4 − 15x^2 − 16 = 0 with u, we get

u^2 - 15u - 16 = 0

( u - 16) (u + 1)

U = 16

U = -1

This is not the end of the problem.

Now we have to substitute x^2 back to u.

x^2 = 16  --> we get the roots 4 and -4

x^2 = -1 --> we get the roots i and -i

tadah!

(0,-3) see attached graph

step-by-step explanation:

a. to solve the system, graph the two equations.

x = y+3 becomes y=x-3 has m=1/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move up 1 unit and 1 unit to the right. plot a point and connect.

y=-4x+3 has m =-4/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move down four units and to the right 1 unit. plot a point and connect.

the solution is the point (x,y) where the two lines intersect. by the graph below it is (0,-3).

b. to solve by substitution, substitute y = -4x-3 into x= y+3

x= (-4x-3) +3

x=-4x

5x=0

x=0

now substitute x = 0 back in to find y.

y= -4(0)-3

y=0-3

y=-3

solution is (0,-3)

c. use elimination by adding the equations together.

x-y=3

4x+y=-3

5x=0

x=0

then substitute into one equation to find y.

y=-4(0)-3

y=-3

i belive those are the ones that are under 90 degreese.