Math Question 10 Points!?

Question

I wrote this incorrectly the last time I asked...

x^4-4x^2 +3

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

Answer 1

I guess you mean you ask us to solve x^4 - 4x^2 +3=0.

I'll do that one :)

This equation is а biquadratic equation, which means it can be solved if you let y=x^2

When you do that, you get a quadratic equation:

y^2 - 4y +3=0

This is solved using either factorizing or the special formulas for quadratic equations, the second one is more general, you probably have learned it in school.

Either way, you get that the roots are y1=1 and y2=3

so we have x^2=1 or x^2=3

which is equivalent to x^2-1=0 or x^2-3=0

(x-1)(x+1)=0 or (x- square root of 3)(x+ square root of 3)=0

Finally, we get four roots of the initial equation:

x1=1, x2=-1, x3=square root of 3, x4= - square root of 3

Answer 2

x^4-4x^2 +3

here we go....

x^4-4x^2 +3 = 0  (set equal to zero)

x^4-4x^2 = -3 (move the 3 over)

x^2 (x + 2) (x - 2) = -3 (take out x^2, & factor)

x^2 = -3 (x+2)= -3 (x-2)= -3 (set each equal to -3)

x^2 = -3 (find square root of -3, but there is not solution for that, so no solution)

(x+2)= -3     (x-2)= -3 (make x alone)

x = -5          x = -1

Then plug both x's into the equation to see if they check.

Once you do that, you see that x = -5 does not check.

But x = -1 does check. So the answer is x = -1.

Hope this helps.

Answer 3

x^4-4x² +3

so you you to solve it like a quadratic equation

and you get(x² -1)(x² -3)=0

x² =1 or x² =3

x=± √ 1  or x=± √ 3

Answer 4

this is a disguised quadratic expression in x^2

let x^2 = p

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

im assuming u want me to solve x^4 - 4x^2 + 3 = 0

so p^2 - 4p + 3 = 0

this equation factorises to give (p - 1)(p - 3)=0

so x^2 = 1 or x^2 = 3

hence x = 1 or -1 and x = sqrt(3) and -sqrt(3)