Question

Given the equation


`y = x(x + 2) - 15`
which of the following inequalities gives all possible true values of x, given that

`y < 0`

Answer choices:

a)

`x > 3`
b)

`0 < x < 3`
c)

`- 5 \leqslant x \leqslant 3`
d)

`- 5 < x < 3`
​

Answer 1

Answer:
`\Large \boldsymbol{d) -5<x<3}`

Step-by-step explanation:

`\displaystyle \Large \boldsymbol {} y=x(x+2)-15 =0 \\\\x^2+2x-15<0 \\\\\left \{ {{x_1+x_2=-2} \atop {\!\!\!\!\!\!x_1x_2=-15}} \right.=> x_1=-5 \ ; \ x_2=3 \\\\\\(x+5)(x-3) <0\\\\\\signs : +++ (-5) --- (3) +++`

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`\Large \boldsymbol{} x \in (-5 \ ; \ 3) \ \ or \ \ -5<x<3`