Q152 / 270 · NDA 2016 (Phase 2) · Mathematics

If $c \gt 0$ and $4 a+c \lt 2 b$, then $a x^2-b x+c=0$ has a root in which one of the following intervals?

  • Correct answer
    A
    $(0,2)$
  • B
    $(2,3)$
  • C
    $(3,4)$
  • D
    $(-2,0)$

Solution

Let $f(x)=a x^2-b x+c$ $\mathrm{f}(2)=4 \mathrm{a}-2 \mathrm{~b}+\mathrm{c} \lt 0$ (given) $\mathrm{f}(0)=\mathrm{c} \gt 0$ (given) So, we can see that sign of $f(x)$ changes, when $x$ changes from 0 to 2 , so it has a root in the interval $(0,2)$.

Hence, the correct answer is option: 'A'.

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