SOLUTION: Solve. 6x^4-7x^2=0 I know I cannot factor and have to use the quadratic formula.
This is what I have but not 100% sure if I am doing my math correctly. Please Help!
-(-7)+ͩ
Algebra.Com
Question 421483: Solve. 6x^4-7x^2=0 I know I cannot factor and have to use the quadratic formula.
This is what I have but not 100% sure if I am doing my math correctly. Please Help!
-(-7)+√(-7)^2-4(6)(2)/2(6) = 7+√1/12 or 7-√1/12
Please let me know if these are correct or not! Thanks sooooo much!
Found 2 solutions by Theo, edjones:
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
you start off with 6x^4 - 7x^2 = 0
factor out an x^2 to get:
x^2 * (6x^2 - 7) = 0
your factors are x^2 and 6x^2 - 7
set x^2 = 0 and you get x = +/- sqrt(0) = 0
set 6x^2 - 7 = 0
add 7 to both sides of the equation to get 6x^2 = 7
divide both sides of the equation by 6 to get x^2 = 7/6
take square root of both sides of equation to get x = +/- sqrt(7/6)
it does not appear that you needed to use the quadratic formula.
your answer should be:
x = 0
x = + sqrt(7/6)
x = - sqrt(7/6)
your original equation is:
6x^4 - 7x^2 = 0
when x = 0, this comes out to be equal to 0.
when x = + sqrt(7/6) this comes out to be 0.
when x = - sqrt(7/6) this also comes out to be 0.
those are your answers.
in order to apply the quadratic equation, you would have had to factor out the x^2 first to get:
x^2 * (6x^2 - 7) = 0
you could then have applied the quadratic formula to 6x^2 - 7 = 0
since the standard form of a quadratic equation is equal to:
ax^2 + bx + c = 0
a would have been 6
b would have been 0
c would have been -7
you would then have applied the quadratic formula to that.
you would have gotten x = +/- sqrt(168)/12
sqrt(168)/12 is equivalent to sqrt(168/144) which is equivalent to sqrt(7/6).
you would have gotten the same answer either way.
x is equal to 0 or x is equal to + sqrt(7/6) or x is equal to - sqrt(7/6).
Answer by edjones(8007) (Show Source): You can put this solution on YOUR website!
6x^4-7x^2=0
x^2(6x^2-7)=0 Factor.
x=0 Ans.
.
6x^2=7
x^2=7/6
x=+-sqrt(7)/sqrt(6)
x=sqrt(7)/sqrt(6) * sqrt(6)/sqrt(6) rationalize the denominator.
=sqrt(42)/6 Ans.
x=-sqrt(42)/6 Ans.
There are 3 answers.
.
Ed
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