Q1. Find the x-intercepts of the equation 3x^2 + 12x + 12 = 0.
Solution:
Using the quadratic formula: a = 3, b = 12, c = 12. Discriminant = 12² - 4(3)(12) = 144 - 144 = 0. x = -b / 2a = -12 / 6 = -2.
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Q2. Find the roots of the equation x^2 - 8x + 16 = 0.
Solution:
This is a perfect square: (x - 4)² = 0. Thus, x - 4 = 0, so x = 4.
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Q3. What is the value of x in the equation x^2 + 2x - 15 = 0?
Solution:
Factoring gives (x - 3)(x + 5) = 0. Thus, x = 3 or x = -5.
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Q4. What is the value of x in the equation 2x^2 - 4x - 6 = 0?
Solution:
Using the quadratic formula x = (-b ± √(b² - 4ac)) / 2a. Here, a = 2, b = -4, c = -6. Discriminant = (-4)² - 4(2)(-6) = 16 + 48 = 64. x = (4 ± √64) / 4 = (4 ± 8) / 4. Thus, x = 3 or x = -1.
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Q5. What is the solution to the inequality x^2 - 4 > 0?
Solution:
Factoring gives (x - 2)(x + 2) > 0. The critical points are x = -2 and x = 2. The solution set is x < -2 or x > 2.
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Q6. What is the solution to the inequality 3x + 5 > 2?
Solution:
Subtract 5 from both sides: 3x > -3. Divide by 3: x > -1.
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Q7. Solve the inequality 3x + 5 > 2.
Solution:
Subtract 5 from both sides: 3x > -3. Divide by 3: x > -1.
