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04 Jun 2025, 00:30
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
65%
(hard)
Question Stats:
57% (01:39) correct
43%
(01:51)
wrong
based on 149
sessions
History
Date
Time
Result
Not Attempted Yet
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
Gentle note to all experts and tutors: Please refrain from replying to this question until the Official Answer (OA) is revealed. Let students attempt to solve it first. You are all welcome to contribute posts after the OA is posted. Thank you all for your cooperation!
A. 0
B. 1
C. 2
D. 3
E. 4
Gentle note to all experts and tutors: Please refrain from replying to this question until the Official Answer (OA) is revealed. Let students attempt to solve it first. You are all welcome to contribute posts after the OA is posted. Thank you all for your cooperation!
04 Jun 2025, 03:09
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let x^2 = y
\(0.1y^2 – 0.5y – 1.4 = 0\)
\(y^2 – 5y – 14 = 0\)
\(y(y – 7)+2(y – 7) = 0\)
\((y+2)(y – 7) = 0\)
y= -2 or y=7
Since y = x^2, considering
y=7 => x^2 = 7
x= 7^{1/2}
So, there is only one value less than 0 for x, which is -7^{1/2}
\(0.1y^2 – 0.5y – 1.4 = 0\)
\(y^2 – 5y – 14 = 0\)
\(y(y – 7)+2(y – 7) = 0\)
\((y+2)(y – 7) = 0\)
y= -2 or y=7
Since y = x^2, considering
y=7 => x^2 = 7
x= 7^{1/2}
So, there is only one value less than 0 for x, which is -7^{1/2}
Bunuel
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
Gentle note to all experts and tutors: Please refrain from replying to this question until the Official Answer (OA) is revealed. Let students attempt to solve it first. You are all welcome to contribute posts after the OA is posted. Thank you all for your cooperation!
A. 0
B. 1
C. 2
D. 3
E. 4
Gentle note to all experts and tutors: Please refrain from replying to this question until the Official Answer (OA) is revealed. Let students attempt to solve it first. You are all welcome to contribute posts after the OA is posted. Thank you all for your cooperation!
04 Jun 2025, 22:01
Kudos
Bookmarks
Bunuel
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
Gentle note to all experts and tutors: Please refrain from replying to this question until the Official Answer (OA) is revealed. Let students attempt to solve it first. You are all welcome to contribute posts after the OA is posted. Thank you all for your cooperation!
Let’s multiply the entire equation by 10. A. 0
B. 1
C. 2
D. 3
E. 4
Gentle note to all experts and tutors: Please refrain from replying to this question until the Official Answer (OA) is revealed. Let students attempt to solve it first. You are all welcome to contribute posts after the OA is posted. Thank you all for your cooperation!
We get, \( 1x^4 – 5x^2 – 14 = 0\)
Let’s us take x^2 = ‘a’ , so the equation becomes \( 1a^2– 5a– 14 = 0\)
\( 1a^2– 5a– 14 = 0\)
\( 1a^2– 7a +2a – 14 = 0\)
\( a(a– 7)+2(a – 7)= 0\)
\( (a-7)*(a+2) = 0\)
hence the values of a = 7, and a = -2
x^2 = 7 , hence X = + sqrt (7) and X = - sqrt (7).
x^2 = -2 , which is not possible. Square of a number remains positive.
for x <0, only ONE value satisfies the equation. X = - sqrt (7).
Thus, Option B
