How do you find the x intercepts of "x^4 -18x^2 +56" ??

Question

Please answer this! Thanks a lot!!

Answer 1

First, I am assuming you meant

y = x^4 -18x^2 +56

Since you want the x intercept, y = 0, so

x^4 -18x^2 +56 = 0

Let a = x^2

a^2 - 18a + 56 = 0

This is now a standard quadratic

(a - 4)(a - 14) = 0

Since a = x^2

(x^2 - 4)(x^2 - 14) = 0

Factorising each bracket

(x + 2)(x - 2)(x + √14)(x - √14) = 0 [Using difference of two squares]

Therefore

x = {±2, ±√14}

Answer 2

This is just a fancy looking quadratic equation... check this out...

if we let m = x^2, then this equation is the following.

m^2 - 18m + 56 = (m - 14)(m - 4)

so to find the x-intercepts... we'd set this equation = to 0
m - 14 = 0
m = 14
x^2 = 14 <-- now let's put x^2 back in
x = +-sqrt(14)

or
m - 4 = 0
m = 4
x^2 = 4
x = +-sqrt(2)

so our x-intercepts are: sqrt(14) ,-sqrt(14),sqrt(2),-sqrt(2)

Answer 3

Make the substitution y=x² and re-write it as
y² - 18y + 56 = 0 and then solve for both values of y (yes, the y values will be complex-valued). Call them Y1 and Y2. Then the 4 roots will be the + and - values of the square roots of the y values. That is
X1 = +√Y1
X2 = -√Y1
X3 = +√Y2
X4 = -√Y2

HTH

Doug

Answer 4

for x^4 -18x^2 +56, substitute x^2 with y:
y^2-18y+56

then factor:
(y-4)(y-14)
y=4 and 14

y=x^2

x^2=4
x=4 or -4

x^2=14
x=square root of 14 or -square root of 14

x=4, -4, square root of 14 or -square root of 14

Answer 5

factor it. if you don't know how to do that, you should ask your mom for help on your homework.