The inequality x2 12x 35 ≥ 0 has two critical points and three possible intervals for solutions. choose each set of possible test points for the three intervals. –8, –6, –4 –10, –6, 0 –6, 0, 6 –6, 0, 10



Answer :

The inequality x2 12x 35 ≥ 0 has two critical points and three possible intervals for solutions.

The given inequality is, x² + 12 x+35≥0

= x²+7 x +5 x+5×7≥0

= x (x+7) +5(x+7)≥0

= (x+5)(x+7)≥0

= x+5=0  ∧ x+7=0 gives x= -7 ∧ x= -5

Now on drawing the number line and marking point ,-5 and -7 on it, we get the following three intervals,  (-∞ , -7], [-7,-5] and [-5,∞).

The solution set of inequality (x+5)(x+7)≥0 is  (-∞ , -7] and [-5,∞).

The set of possible test points for

⇒ (-∞ , -7] = -8,  -10

⇒ [-7,-5] = -6

⇒ [-5,∞) = -4, 0

Option (1) -8,-6,-4 and Option (2) -10,-6,0 satisfy the given condition.

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