SOLUTION: Find four roots of the following equation:
2x^4 +5x^2 = 207
* I plugged into my calculator and only got 2 roots, x=-3 and x=3, but how do you get the rest? Thanks :)
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-> SOLUTION: Find four roots of the following equation:
2x^4 +5x^2 = 207
* I plugged into my calculator and only got 2 roots, x=-3 and x=3, but how do you get the rest? Thanks :)
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Question 1013018: Find four roots of the following equation:
2x^4 +5x^2 = 207
* I plugged into my calculator and only got 2 roots, x=-3 and x=3, but how do you get the rest? Thanks :) Found 4 solutions by ikleyn, stanbon, macston, MathLover1:Answer by ikleyn(52788) (Show Source):
You can put this solution on YOUR website! .
Find four roots of the following equation:
2x^4 +5x^2 = 207
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Introduce new variable for your convenience, y = .
Then your equation takes the form
= .
Apply the quadratic formula. You will get
= = = .
So, = 9, = .
Now you need to solve this two quadratic equations:
1) = 9. It has two solutions: x = and x = .
2) = . It has two solutions: x = and x = .
Thus you got four solutions of your original equation.
You can put this solution on YOUR website! Find four roots of the following equation:
2x^4 +5x^2 = 207
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Divide by x^2-9 to get 2x^2 + 23
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Solve 2x^2 + 23 = 0
2x^2 = -23
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x^2 = -11.5
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x = isqrt(11.5) or x = -isqrt(11.5)
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Cheers,
Stan H.
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You can put this solution on YOUR website! .
Let y=x^2
.
2x^4+5x^2=207 . Replace x^2 with y.
2y^2+5y-207=0
(y-9)(2y+23)=0
y-9=0 . or . 2y+23=0
y=9 . or . 2y=-23
y=9 . or . y=-23/2 . Replace y with x^2
x^2=9 . or . x^2=-23/2
x=+/- 3 . or x=+/-i=+/-
You can put this solution on YOUR website! write in standard form
Factor:
The first term is, its coefficient is .
The middle term is, its coefficient is .
The last term, "the constant", is
Multiply the coefficient of the first term by the constant
Find two factors of whose sum equals the coefficient of the middle term, which is : these are and
Rewrite the polynomial splitting the middle term using the two factors found above, and :
............group first two terms together and second two terms together
solutions:
if => => =>=>
two complex solutions are: and
if => => =>
two real solutions: and
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