Solve the quadratic equation. x^4 -3x^2 -4= 0. How???

Question

x^2 means x squared
x^4 means x quadrupled

Answer 1

x^4 -3x^2 -4= 0
x^4 - 4x^2 + x^2 - 4 = 0
x^2 (x^2 - 4) + 1(x^2 - 4) = 0
(x^2 - 4) (x^2 +1) = 0

Therefore
Either x^2 - 4 = 0
x^2 = 4
x = +2 or -2

Or x^2 +1 = 0
x^2 = -1
Since squares cannot be negative (unless you want to get involved with imaginary numbers)

x = +2 or x = -2

Answer 2

Quartic equations have the general form:
a X4 + bX 3 + cX2 + dX + e = 0


Example # 1
Quartic Equation With 4 Real Roots
3X4 + 6X3 - 123X2 - 126X + 1,080 = 0
Quartic equations are solved in several steps. First, we simplify the equation by dividing all terms by 'a', so the equation then becomes:


X4 + 2X 3 - 41X2 - 42X + 360 = 0

Where a = 1 b = 2 c = -41 d = -42 and e = 360
Next we define the variable 'f':

f = c - (3b2/8)
"Plugging in" the numbers from the above equation, we get:

f = -41 - (3*2*2/8)
f = -42.5
Next we define 'g':

g = d + (b3 / 8) - (b*c/2)
"Plugging in" the numbers:
g = -42 + (8/8) - (2 * -41 / 2)
g = 0
Next, we define 'h':

h = e - (3*b4/256) + (b 2 * c/16) - ( b*d/4)
Plugging in the numbers:

h = 370.5625


Next, we "plug" the numbers 'f', 'g' and 'h' into the following cubic equation:

Y3 + (f/2)*Y2 + ((f2 -4*h)/16)*Y -g2/64 = 0
Y3 -21.25*Y2 + (1,806.25 -4 * 370.5625 )/16*Y -02/64 = 0
Y3 -21.25*Y2 + (1,806.25 -1,482.25)/16*Y -02/64 = 0
Y3 -21.25*Y2 + 20.25*Y -0 = 0
Next, we solve this cubic equation by using the method located at solving cubic equations OR (much easier) using the

CUBIC EQUATION CALCULATOR.
And the 3 roots of the equation are:

Y1= 20.25 Y2= 0 Y3= 1
Let 'p' and 'q' be the square roots of ANY 2 non-zero roots (Y1 Y2 or Y3).


p=SqRoot(20.25) = 4.5

q=SqRoot(1) = 1

r= -g/(8*pq) = 0

s= b/(4*a) = 6/(4*3) = 0.5
Then the four roots of the quartic equation are:

X1= p + q + r -s = 4.5 + 1 + 0 - .5 = 5
X2= p - q - r -s = 4.5 - 1 - 0 - .5 = 3
X3= -p + q - r -s = -4.5 + 1 - 0 - .5 = -4
X4= -p - q + r -s = -4.5 - 1 + 0 - .5 = -6

Answer 3

It is not quadratic equation, since maximum power of x = 4

The given equation can be factorised.

x^4 - 3x^2 - 4 = 0

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

x^2(x^2 - 4) + 1(x^2-4) = 0

(x^2+1) (x^2-4) = 0

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

so x = 2, -2 or +/- i

Answer 4

x^4 -3x^2 -4 = 0
x^4 -4x^2 +x^2 -4 = 0
x^2(x^2 -4) +1(x^2 -4) = 0
(x^2 +1)(x^2 -4) = 0
x^2 = 4 OR x^2 = -1
x = +2, -2 OR x = i, -i
x = 2,-2,i,-i

The graph of this equations is a quartic function.
Also, as it has positive sign, it will be 'W' shaped with graph touching x-axis only twice because the other two roots are non-real or complex roots.

Answer 5

Factor it as a quadratic in x²:
(x²-4)(x²+1) = 0.
So x² = 4,
x = -2 or 2
x² = -1
x = i or -i.
BTW. This is a quartic, quadratic in form,
so it has 4 roots.

Answer 6

graph it on a graphing calc and see where the line crosses the x axis
answer is (2,-2)
or you can factor it into (x^2+1)(x^2-4)
then set x^2+1 to equal 0
solve for x
repeat step above but use x^2-4
x^2+1 won't give a real answer so you have to use x^2-4
x^2-4=0
x^2=4
x=+or- square root 4 which is 2
x=(2,-2)

Answer 7

= (x^2 - 4)(x^2 +1) = 0
= (x - 2)(x + 2)(x^2 + 1) = 0
x = 2 x = -2

Answer 8

x^4 - 3x^2 - 4 = 0

(x^2 - 4)(x^2 + 1) = 0 {factor the trinomial}

(x + 2)(x - 2)(x^2 + 1) = 0 {factor diff of 2 squares}

Now

x + 2 = 0
x = -2

x - 2 = 0
x = 2

x^2 + 1 = 0
x^2 = -1
x = +- i

Answer 9

4X2 - x + 5=0 (4x - 5)(x + 1) = 0 4x - 5 = 0 --> 4x = 5 --> x = 5/4 x + 1 = 0 --> x = -1 x = 5/4 and x = -1 are the only solutions x2 - kx + 4 = 0 Just solve the equation and make up the number ex. (x + 4)(x + 1) = 0 k = 5 x4 - 5x2 - 36 = 0 (x2 - 9)(x2 + 4) = 0 x2 - 9 = 0 x2 = 9 --> x = 3 x = -3 x2 + 4 = 0 x2 = -4 FALSE (A number squared can never be negative) 3 and -3 are only solution Go to my profile page and e-mail if you want me to show work on paper

Answer 10

i want to remind you that the equation you have given is not a quadratic equation.It is because the maximum power of x is 4. To be a quadratic equation x should have power equal to 2.

Mind it the form of equation ax^2+bx+c=0 (where a is not equal to 0) is a quardatic equation.