Math Question...10 points!?

Question

x^4-4x^2 +3

Whoever gets it right and shows work gets 10 points...thanks for help guys

Answer 1

x^4-4x^2 +3=

x^4-x^2-3x^2+3=

(x^2-1)(x^2-3)=

(x-1)(x+1)(x^2-3)

Answer 2

This equation can be factored as

(x^2 - 3)(x^2 - 1) = 0

So we have x^2 - 3 = 0, which leads to x = sqrt(3) and x = -sqrt(3).

Or (X^2 - 1) = 0, which leads to x = 1 and x = -1.

Answer 3

(x^2-3)(x^2-1). There's no more work to show.

Answer 4

that's hard i am a six grader

Answer 5

5 soz im not good with working out

Answer 6

x^4-4x^2 +3

You need two numbers that multiply to be +3, and add up to -4. Those two numbers are -3 and -1.

Using that you can plug them in into (x + a)(x + b) if (x + a)(x + b) = x^2 + ax + bx + ab.

But your x is to the fourth power, so you would need to find the square root of that which is x^2.

(x^2 + a)(x^2 + b)

a = -1, b = -3

(x^2 - 1)(x^2 - 3)

But you have a difference of squares. (x^2 - 1)

The formula for that is (x^2 - y^2) = (x + y)(x - y)

Therefore, your problem turns into (x + 1)(x - 1)(x^2 - 3).

If you want to solve that if x^4-4x^2 +3=0, then you need to set the factored part equal to 0.

(x + 1)(x - 1)(x^2 - 3) = 0

Since they are quantities multiplied to equal zero, you can divide the entire problem by two of the quantities and your remaining quanitity will equal zero.

[(x + 1)(x - 1)(x^2 - 3)]/[(x - 1)(x^2 - 3)] = 0

(x + 1) = 0

[(x + 1)(x - 1)(x^2 - 3)]/[(x + 1)(x - 1)] = 0

(x^2 - 3) = 0

[(x + 1)(x - 1)(x^2 - 3)]/[(x + 1)(x^2 - 3)] = 0

(x - 1) = 0

(x + 1) = 0

x + 1 - 1 = 0 -1

x = -1

(x - 1) = 0

x - 1 + 1 = 0 + 1

x = 1

(x^2 - 3) = 0

x^2 - 3 + 3 = 0 + 3

x^2 = 3

x = (negative or positive square root of three)

x = +√3 , -√3

So your final answer is x = 1, -1, +√3 , -√3.

I hope this helps. Now don't be cheating on your math homework. I hope you can do later homework following some of these procedures.  

Answer 7

(x^2 - 1)*(x^2 - 3) = 0

x^2 - 1 = 0       OR      x^2 - 3 = 0

x^2 = 1            OR      x^2 = 3

x = +1 or -1     OR      x = +√3 or -√3