Determine Roots/Zeroes

Question

The equation x^4−5x^2+6=0 has four solutions. Place the four solutions in increasing order in decimal form.

I already have 1) −1.732050808 2) ? 3) 1.414213562 4) ?

Answer 1

This equation is quadratic in terms of x². It can be factored as:

(x² - 3)(x² - 2) = 0

That means:

x² = 3 or x² = 2.

Solve each of those for x by using the square root property:

x = ±√3 or x=±√2

Those are the 4 exact roots.

In order from smallest to largest:

-1.732, -1.414 , 1.414, 1,732 (those are only listed to 3 decimal places)

Check it out here:

desmos.com/calculator/3ed5u1vbds

Answer 2

x^4 -5x^2 + 6 = 0

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

x^2 = 2 or 3

x = +/-sqr2 or 3

x = about -1.414,+1.414, -1.732, or +1.732

or if you can't factor use the quadratic formula

x^2 = 5/2 +/-.5sqr(25-4(6)) = 2.5+/-1/2 = 2 or 3

x =+/-sqr2 or 3

= +/-1.414 or +/-1.732 approximately