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NDA 2016
Exam
NDA
Year
2016
Subject
Mathematics
Chapter
Quadratic Equation

NDA 2016 · Mathematics · Quadratic Equation

If c > 0 and 4 a+c < 2 b , then a x^2-b x+c=0 has a root in which...

If c>0c > 0 and 4a+c<2b4 a+c < 2 b, then ax2−bx+c=0a x^2-b x+c=0 has a root in which one of the following intervals?

Options

  1. A(0,2)(0,2)
  2. B(2,3)(2,3)
  3. C(3,4)(3,4)
  4. D(−2,0)(-2,0)

Correct answer

A. (0,2)(0,2)

Step-by-step solution

Let f(x)=ax2−bx+cf(2)=4a−2b+c<0f(x)=a x^2-b x+c\mathrm{f}(2)=4 \mathrm{a}-2 \mathrm{ b}+\mathrm{c} < 0 (given) f(0)=c>0\mathrm{f}(0)=\mathrm{c} > 0 (given) So, we can see that sign of f(x)f(x) changes, when xx changes from 0 to 2 , so it has a root in the interval (0,2)(0,2).
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