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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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19 Sep 2018, 20:14
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Difficulty:

65% (hard)

Question Stats:

46% (01:32) correct 54% (01:45) wrong based on 41 sessions

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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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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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20 Sep 2018, 07:40
Top Contributor
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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# For how many values of x<0 does the equation 0.1x^4 – 0.5x^2 – 1.4 = 0

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