Hard math questions
Harder quadratic and algebraic challenges for advanced practice.
A collection of hard math problems and hard math questions with answers, pulled out from easier practice sets for anyone who wants the hardest math question available rather than a mix of difficulties.
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Sample Hard math questions
1. Solve: 3x^2 + 3x - 60 = 0+
Answer: x = -5 or x = 4
Step 1: Identify a = 3, b = 3, c = -60. Step 2: Compute the discriminant: b^2 - 4ac = 3^2 - 4(3)(-60) = 729. Step 3: Apply the quadratic formula: x = (-b ± √discriminant) / 2a = (-3 ± 27) / 6. Step 4: x = -5 or x = 4.
2. Solve: 5x^2 + 10x - 15 = 0+
Answer: x = -3 or x = 1
Step 1: Identify a = 5, b = 10, c = -15. Step 2: Compute the discriminant: b^2 - 4ac = 10^2 - 4(5)(-15) = 400. Step 3: Apply the quadratic formula: x = (-b ± √discriminant) / 2a = (-10 ± 20) / 10. Step 4: x = -3 or x = 1.
3. Solve: 6x^2 - 96 = 0+
Answer: x = 4 or x = -4
Step 1: Identify a = 6, b = 0, c = -96. Step 2: Compute the discriminant: b^2 - 4ac = 0^2 - 4(6)(-96) = 2304. Step 3: Apply the quadratic formula: x = (-b ± √discriminant) / 2a = (0 ± 48) / 12. Step 4: x = 4 or x = -4.
4. Solve: 3x^2 + 21x + 36 = 0+
Answer: x = -3 or x = -4
Step 1: Identify a = 3, b = 21, c = 36. Step 2: Compute the discriminant: b^2 - 4ac = 21^2 - 4(3)(36) = 9. Step 3: Apply the quadratic formula: x = (-b ± √discriminant) / 2a = (-21 ± 3) / 6. Step 4: x = -3 or x = -4.
5. Solve: 9x^2 + 72x + 144 = 0+
Answer: x = -4
Step 1: Identify a = 9, b = 72, c = 144. Step 2: Compute the discriminant: b^2 - 4ac = 72^2 - 4(9)(144) = 0. Step 3: Apply the quadratic formula: x = (-b ± √discriminant) / 2a = (-72 ± 0) / 18. Step 4: x = -4.
6. Solve: 2x^2 - 14x + 24 = 0+
Answer: x = 4 or x = 3
Step 1: Identify a = 2, b = -14, c = 24. Step 2: Compute the discriminant: b^2 - 4ac = (-14)^2 - 4(2)(24) = 4. Step 3: Apply the quadratic formula: x = (-b ± √discriminant) / 2a = (14 ± 2) / 4. Step 4: x = 4 or x = 3.