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Let [x] denote the greatest integer function. What is the number of solutions of the equation x2 + 4x + [x] = 0 in the interval [0,2]?
- a)Zero (no solution)
- b)One
- c)Two
- d)Three
Correct answer is option 'A'. Can you explain this answer?
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Let [x] denote the greatest integer function. What is the number of so...
No. of solution = one
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Let [x] denote the greatest integer function. What is the number of so...
Solution:
Given equation is x^2 + 4x [x] = 0.
Let [x] = k, where k is an integer.
Then k ≤ x < k="" +="" />
Therefore, k^2 + 4k = 0.
⇒ k(k + 4) = 0.
⇒ k = 0 or -4.
If k = 0, then 0 ≤ x < />
If k = -4, then -4 ≤ x < />
Since the interval [0,2] does not contain any value of x such that -4 ≤ x < -3,="" there="" are="" no="" solutions="" to="" the="" given="" equation="" in="" the="" interval="" />
Hence, the correct option is (a) Zero (no solution).
Given equation is x^2 + 4x [x] = 0.
Let [x] = k, where k is an integer.
Then k ≤ x < k="" +="" />
Therefore, k^2 + 4k = 0.
⇒ k(k + 4) = 0.
⇒ k = 0 or -4.
If k = 0, then 0 ≤ x < />
If k = -4, then -4 ≤ x < />
Since the interval [0,2] does not contain any value of x such that -4 ≤ x < -3,="" there="" are="" no="" solutions="" to="" the="" given="" equation="" in="" the="" interval="" />
Hence, the correct option is (a) Zero (no solution).
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Let [x] denote the greatest integer function. What is the number of solutions of the equation x2 + 4x + [x] = 0 in the interval [0,2]?a)Zero (no solution)b)Onec)Twod)ThreeCorrect answer is option 'A'. Can you explain this answer?
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