Find all values of m for which the inequality mx2 - 4x + 3m + 1 > 0 is satisfied for all +ve values of x

We havem>0 and D 0(3m+4)(m−1)>0m 1Hence, the solution is m∈(1,∞)

Find all values of m for which the inequality mx2 - 4x + 3m + 1 > 0 is satisfied for all +ve values of x

We havem>0 and D 0(3m+4)(m−1)>0m 1Hence, the solution is m∈(1,∞)

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Find all values of m for which the inequality mx² - 4x + 3m + 1 > 0 is satisfied for all +ve values of x

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$m = (1, \infty)$

$m \in (5, \infty)$

$m \in (1, \infty)$

answer is D.

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Detailed Solution

We have

$\begin{array}{l} m > 0 and D < 0 \\ 16 - 4 m (3 m + 1) < 0 \\ 3 m^{2} + m - 4 > 0 \\ (3 m + 4) (m - 1) > 0 \\ m < - \frac{4}{3} and m > 1 \end{array}$

Hence, the solution is $m \in (1, \infty)$

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Find all values of m for which the inequality mx2 - 4x + 3m + 1 > 0 is satisfied for all +ve values of x

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Find all values of m for which the inequality mx² - 4x + 3m + 1 > 0 is satisfied for all +ve values of x