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Most Important Selected Qs for JEE AdvancedMathematicsQuadratic Equation

Let f(x)=p x^2-3 p x+14 . If f(x) |3 -4 | x, R , then identify which of the following statement(s) is/are correct?

Options

  1. ASum of all possible integral values of p is 10 .
  2. BSum of all possible integral values of p is 15 .
  3. CIf f(x) 14+ ^2 x, R then number of integral value of p is 1 .
  4. DIf f(x) 14+ ^2 x, R then number of integral value of p is 0 .

Correct answer

C. If f(x) 14+ ^2 x, R then number of integral value of p is 1 .

Step-by-step solution

p x^2-3 p x+14 |3 -4 | x, R array ll & p x^2-3 p x+14 5 x R & p x^2-3 p x+9 0 & p>0, D 0 9 p^2-4 p 9 0 & p(p-4) 0 p [0,4] & p [0,4] array For p=0, f(x)=14 5 Sum of integral values of p=10 . Now, f(x) 14+ ^2 x, a Rp=0 is only the possible value.

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