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If $\mathrm{c}>0$ and $4 \mathrm{a}+\mathrm{c} < 2 \mathrm{~b}$, then $\mathrm{ax}^{2}-\mathrm{bx}+\mathrm{c}=0$ has a root in
which one of the following intervals?
Options:
which one of the following intervals?
Solution:
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Verified Answer
The correct answer is:
$(0,2)$
Let $\mathrm{f}(\mathrm{x})=\mathrm{ax}^{2}-\mathrm{bx}+\mathrm{c}$
$\mathrm{f}(2)=4 \mathrm{a}-2 \mathrm{~b}+\mathrm{c} < 0 \quad$ (given)
$f(0)=c>0 \quad$ (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 $(0,2) .$
$\mathrm{f}(2)=4 \mathrm{a}-2 \mathrm{~b}+\mathrm{c} < 0 \quad$ (given)
$f(0)=c>0 \quad$ (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 $(0,2) .$
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