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NTA Abhyas 2020
Exam
NTA Abhyas
Year
2020
Subject
Mathematics
Chapter
Quadratic Equation

NTA Abhyas 2020 · Mathematics · Quadratic Equation

If f (x) = ∏ _ k = 1 ^ 999 (x^ 2 - 47x + k) , then product of all...

If ff\left(x\right)=∏k=1999(x2−47x+k)= {∏}_{k = 1}^{999} \left(x^{2} - 47x + k\right), then product of all real roots of f\left(x\right)=0=0 is

Options

  1. A550!550 !
  2. B551!551 !
  3. C552!552 !
  4. D999!999 !

Correct answer

C. 552!552 !

Step-by-step solution

Consider x2−47x+k=0x^{2} - 47x + k = 0

For real roots, 472−4k≥0⇒k≤552{47}^{2} - 4k \ge 0 ⇒ k \le 552

∴k=1,2,3….,552∴ k = 1, 2, 3 \ldots. , 552

Product of real roots =1×2×3×4×…..×552=552!= 1 \times 2 \times 3 \times 4 \times \ldots.. \times 552 = 552 !
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