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NDA 2020
Exam
NDA
Year
2020
Subject
Mathematics
Chapter
Quadratic Equation

NDA 2020 · Mathematics · Quadratic Equation

If f(x)=3 x^2-5 x+p and f(0) and f(1) are opposite in sign, then...

If f(x)=3x2−5x+pf(x)=3 x^2-5 x+p and f(0)f(0) and f(1)f(1) are opposite in sign, then which of the following is correct?

Options

  1. A−2<p<0-2 < p < 0
  2. B−2<p<2-2 < p < 2
  3. C0<p<20 < p < 2
  4. D3<p<53 < p < 5

Correct answer

C. 0<p<20 < p < 2

Step-by-step solution

f(0)=3(0)2−5(0)+P=Pf(1)=3(1)2−5(1)+P=P−2f(0)=3(0)^2-5(0)+P=Pf(1)=3(1)^2-5(1)+P=P-2 Clearly, f(0)f(0) and f(1)f(1) are opposite in sign. ∴P>0\therefore P > 0 and P−2<0P-2 < 0. ⇒0<P<2\Rightarrow 0 < P < 2
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