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If f (x) = x– 4x + p, and f (0) and f(1) are of opposite signs, then which of the following is necessarily true?
  • a)
    –1 < p < 2
  • b)
    0 < p < 3
  • c)
    –2 < p < 1
  • d)
    –3 < p < 0
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
If f (x) = x3– 4x + p, and f (0) and f(1) are of opposite signs,...
f(0) = p
f (1) = 1 – 4 + p = p + 3.
p and p+3 are of different signs.
Substitute for the options: 
1st option, if p is a negative number, then p – 3 is also negative, and both are same sign.
For 3rd and 4th option, also it is the same.
For the 2nd option, value of p is between 0 and 3, and p – 3 is negative. Hence it agrees.
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Most Upvoted Answer
If f (x) = x3– 4x + p, and f (0) and f(1) are of opposite signs,...
If f(x) = x^3, then f(x) represents a function where the input value (x) is raised to the power of 3. This means that for any given value of x, the function will return the cube of that value.
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If f (x) = x3– 4x + p, and f (0) and f(1) are of opposite signs, then which of the following is necessarily true?a)–1 < p < 2b)0< p < 3c)–2 < p < 1d)–3 < p < 0Correct answer is option 'B'. Can you explain this answer?
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