CLAT Exam > CLAT Questions > If y2+ 3y – 18 ≥ 0, which of the fol...
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If y2 + 3y – 18 ≥ 0, which of the following is true?
- a)y ≤ 3 or y ≥ 0
- b)y ≥ 3 or y ≤ – 6
- c)-6 ≤ y ≤ 3
- d)y > – 6 or y < 3
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
If y2+ 3y – 18 ≥ 0, which of the following is true?a)y ≤ 3...
y2 + 3y - 18 ≥ 0
⇒ y2 + 6y - 3y - 180
⇒ y(y + 6) -3(y + 6) ≥ 0
⇒ (y - 3)(y + 6) ≥ 0
⇒ y ≥ 3andy ≤ - 6
Most Upvoted Answer
If y2+ 3y – 18 ≥ 0, which of the following is true?a)y ≤ 3...
Understanding the Inequality
The given inequality is y^2 + 3y - 18 ≥ 0. To solve this inequality, we need to find the values of y that satisfy this condition.
Factoring the Quadratic Expression
First, we factor the quadratic expression y^2 + 3y - 18 to (y + 6)(y - 3) ≥ 0. This helps us identify the critical points where the expression changes sign.
Finding Critical Points
The critical points are where the expression equals zero, which are y = -6 and y = 3. These points divide the number line into three intervals: (-∞, -6), (-6, 3), and (3, ∞).
Testing Intervals
We can now test each interval to see when the inequality holds true.
- For y < -6,="" both="" factors="" are="" negative,="" so="" the="" inequality="" is="" />
- For -6 < y="" />< 3,="" one="" factor="" is="" negative="" and="" one="" is="" positive,="" making="" the="" inequality="" />
- For y > 3, both factors are positive, so the inequality is true.
Final Answer
Therefore, the values of y that satisfy the inequality y^2 + 3y - 18 ≥ 0 are y ≥ 3 or y ≤ -6. This corresponds to option B: y ≥ 3 or y ≤ -6.
The given inequality is y^2 + 3y - 18 ≥ 0. To solve this inequality, we need to find the values of y that satisfy this condition.
Factoring the Quadratic Expression
First, we factor the quadratic expression y^2 + 3y - 18 to (y + 6)(y - 3) ≥ 0. This helps us identify the critical points where the expression changes sign.
Finding Critical Points
The critical points are where the expression equals zero, which are y = -6 and y = 3. These points divide the number line into three intervals: (-∞, -6), (-6, 3), and (3, ∞).
Testing Intervals
We can now test each interval to see when the inequality holds true.
- For y < -6,="" both="" factors="" are="" negative,="" so="" the="" inequality="" is="" />
- For -6 < y="" />< 3,="" one="" factor="" is="" negative="" and="" one="" is="" positive,="" making="" the="" inequality="" />
- For y > 3, both factors are positive, so the inequality is true.
Final Answer
Therefore, the values of y that satisfy the inequality y^2 + 3y - 18 ≥ 0 are y ≥ 3 or y ≤ -6. This corresponds to option B: y ≥ 3 or y ≤ -6.
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If y2+ 3y – 18 ≥ 0, which of the following is true?a)y ≤ 3 or y ≥ 0b)y ≥ 3 or y ≤ – 6c)-6 ≤ y ≤ 3d)y > – 6 or y < 3Correct answer is option 'B'. Can you explain this answer?
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