Question

The inequality x + 12x + 35 has two critical points and three possible intervals for solutions. Choose

Answer 1

Answer:

Option 1 and 2.

Step-by-step explanation:

Consider he given inequality is

$x^2 + 12 x+35\ge0$

Splitting the middle term we get

$x^2 +7x+5x+35\ge0$

$x(x+7)+5(x+7)\ge0$

$(x+5)(x+7)\ge0$

The related equation is

$(x+5)(x+7)=0$

Using zero product property we get

$x+5=0\Rightarrow x=-5$

$x+7=0\Rightarrow x=-7$

Draw number line and mark -5 and -7 on it.

Now the three intervals are (-∞ , -7], [-7,-5] and [-5,∞).

The set of possible test points for

⇒ (-∞ , -7] → -8,  -10

⇒ [-7,-5] → -6

⇒ [-5,∞) → -4, 0, 4, 6

-8,-6,-4 and -10,-6,0 satisfies the given condition.

Therefore, the correct options are 1 and 2.