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23 Feb 2017, 08:10
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Which of the following must equal zero for all real numbers x ?
I. x^3 - x^2
II. x^0
III x^1
A. None.
B. I only
C. II only
D. I and II only
E. II and III only
I. x^3 - x^2
II. x^0
III x^1
A. None.
B. I only
C. II only
D. I and II only
E. II and III only
23 Feb 2017, 08:22
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vikasp99
Which of the following must equal zero for all real numbers x ?
I. x^3 - x^2
II. x^0
III x^1
A. None.
B. I only
C. II only
D. I and II only
E. II and III only
I. x^3 - x^2
II. x^0
III x^1
A. None.
B. I only
C. II only
D. I and II only
E. II and III only
I. x^3 - x^2 = 0 ( Only when x = 1 ; for all other values of x the result in not zero )
II. x^0 = 1 ( For all values of x )
III. x^1 = x ( For all values of x )
Thus, None of the given options hold good, answer will be (A)
23 Feb 2017, 08:42
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vikasp99
Which of the following must equal zero for all real numbers x ?
I. x^3 - x^2
II. x^0
III x^1
A. None.
B. I only
C. II only
D. I and II only
E. II and III only
I. x^3 - x^2
II. x^0
III x^1
A. None.
B. I only
C. II only
D. I and II only
E. II and III only
This is a MUST question, which means if an expression can be shown to NOT EQUAL ZERO, we can eliminate it.
I. x^3 - x^2
Test a value.
For example, when x = 2, x^3 - x^2 = 2^3 - 2^2 = 8 - 4 = 4
Since x^3 - x^2 DOES NOT EQUAL ZERO we can eliminate statement I
II. x^0
Test a value.
For example, when x = 2, x^0 = 2^0 = 1
Since x^0 DOES NOT EQUAL ZERO we can eliminate statement II
III. x^1
Test a value.
For example, when x = 1, x^1 = 1^1 = 1
Since x^1 DOES NOT EQUAL ZERO we can eliminate statement III
Answer: A
