For what values of $x$ is the expression $15 + 4 x - 3 x^{2}$ negative?

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Solution

$15 + 4 x - 3 x^{2} < 0$
$\Rightarrow 15 + 9 x - 5 x - 3 x^{2} < 0$
$\Rightarrow 3 (5 + 3 x) - x (5 + 3 x) < 0$
$\Rightarrow (5 + 3 x) (3 - x) < 0$
$\Rightarrow (x - 3) (3 x + 5) > 0$ , multiply both sides by $- 1$ , sign will change
$\Rightarrow x \in (- \infty, - \frac{5}{3}) \cup (3, \infty)$ , use wavy curve method

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Similar questions

| 2 x + 3 y | < 15

A: The minimum value of 'y' for the expression y = 2 $x^{2}$ + 4x + 5 occur at x =______

B: The maximum value of expression -3 $x^{2}$ + 12x + 5 is _______

m

(2 m - 3) x^{2} - 4 x + (2 m - 3) = 0

x^{2} - 4 x - 32

3 (x^{2} - 4 x)

x = 5

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