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For how many values of x<0 does the equation 0.1x^4 – 0.5x^2 – 1.4 = 0

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For how many values of x<0 does the equation 0.1x^4 – 0.5x^2 – 1.4 = 0  [#permalink]

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New post 19 Sep 2018, 20:14
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Question Stats:

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For how many values of \(x < 0\) does the equation \(0.1x^4 – 0.5x^2 – 1.4 = 0\) hold?

A. 0

B. 1

C. 2

D. 3

E. 4

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For how many values of x<0 does the equation 0.1x^4 – 0.5x^2 – 1.4 = 0  [#permalink]

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New post 19 Sep 2018, 20:24
workout wrote:
For how many values of \(x < 0\) does the equation \(0.1x^4 – 0.5x^2 – 1.4 = 0\) hold?

A. 0

B. 1

C. 2

D. 3

E. 4


\(0.1x^4 – 0.5x^2 – 1.4 = 0\)
or , \(x^4 – 5x^2 – 14 = 0\)
or , \((x^2 - 7) (x^2 + 2) = 0\)
Now, \(x^2 + 2\) NE \(0\), as \(x^2\) is +ve.
Therefore, \(x^2 - 7 = 0\)==> \(x= + \sqrt{7} , - \sqrt{7}\)
Hence only \(1\) value of \(x\) (\(- \sqrt{7}\)) is LT \(0\)......... Ans B
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Re: For how many values of x<0 does the equation 0.1x^4 – 0.5x^2 – 1.4 = 0  [#permalink]

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New post 20 Sep 2018, 07:40
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workout wrote:
For how many values of \(x < 0\) does the equation \(0.1x^4 – 0.5x^2 – 1.4 = 0\) hold?

A. 0

B. 1

C. 2

D. 3

E. 4


GIVEN: 0.1x⁴ – 0.5x² – 1.4 = 0
Multiply both sides by 10 to get: x⁴ – 5x² – 14 = 0

ASIDE: This expression behaves like a quadratic expression in that, if we let k = x², we COULD rewrite it as k² - 5k - 14 = 0, which can be factored as: (k - 7)(k + 2) = 0

Okay, back to the equation...
Factor the left side to get: (x² - 7)(x² + 2) = 0
So, either (x² - 7) = 0 or (x² + 2) = 0

Let's examine each case...

If x² - 7 = 0, then x² = 7
So, either x = √7 or x = -√7

If x² +2 = 0, then x² = -2
This equation has no solution, since x² must be greater than or equal to zero.

So, there are only 2 possible solutions: x = √7 and x = -√7
However, the question tells us that x < 0, which means there's only ONE solution: x = -√7

Answer: B

Cheers,
Brent
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Re: For how many values of x<0 does the equation 0.1x^4 – 0.5x^2 – 1.4 = 0 &nbs [#permalink] 20 Sep 2018, 07:40
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