Question

Graph f(x)=5x^4+15x^2+10 and use the graph to approximate any zeros (accurate to 3 decimal places) and find zeros algebraically

Answer 1

To find zeros algebraically, put x^2 = t and you will get a quadratic equation in t which you can solve.

Answer 2

what do you mean? where are you getting the t from?

Answer 3

To find the zeros of f(x)=5x^4+15x^2+10 we need to solve
5x^4+15x^2+10 = 0
This is a fourth degree polynomial and as such it is not easy to solve. But if you recognize this as a quadratic formula in x^2 then we know how to solve a quadratic equation. To make it easy we let t = x^2 and the original equation becomes:
5t^2 + 15t + 10 = 0 (which is a quadratic equation in t). Solve for t first and then put back x^2 in the place of t and solve for x.

Answer 4

would t = 0?

Answer 5

5t^2 + 15t + 10 = 0
5(t^2 + 3t + 2) = 0
5(t+1)(t+2) = 0
t = -1 or t = -2
put t = x^2
x^2 = -1 and x^2 = -2
Since a square number is negative there are no real solutions for x. So the graph of this function will never cut the x axis because it has no real zeros.
But it has complex zeros. +i, -i, +sqrt(2)i and - sqrt(2)i

Answer 6

thank you @ranga ! but what about the part that says to approzimate any zeros accurate to 3 decimal places??

Answer 7

Since there are no real zeros, there is nothing to be done there.

Answer 8

oh okay, thank you :)

Answer 9

You are welcome.