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Trick Spotter: I. x² + 11x + 28 = 0 II. y² − 8y + 15 = 0. Which is the fastest correct way to compare x and y?

Correct Answer: B [Sign Rule: both x-roots are negative and both y-roots are positive, so x < y]

Explanation:

b and c both plus → x-roots negative (−4, −7); b minus, c plus → y-roots positive (3, 5) → x < y with no solving.

Reverse question: one root of x² + px + 30 = 0 is 5. What is the value of p?

Correct Answer: A [−11]

Explanation:

Product of roots = 30 → other root 6; sum = 11 = −p → p = −11.

For x² − 9x + 14 = 0, which of the following is/are correct?
I. The sum of the roots is 9.
II. The product of the roots is −14.
III. Both roots are positive.

Correct Answer: C [Only I and III]

Explanation:

Roots 2 and 7: sum 9 ✓, product 14 (not −14) ✗, both positive ✓.

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Online Quiz

Correct Answer: B [Sign Rule: both x-roots are negative and both y-roots are positive, so x < y]

Explanation:

b and c both plus → x-roots negative (−4, −7); b minus, c plus → y-roots positive (3, 5) → x < y with no solving.

Correct Answer: A [−11]

Explanation:

Product of roots = 30 → other root 6; sum = 11 = −p → p = −11.

Correct Answer: C [Only I and III]

Explanation:

Roots 2 and 7: sum 9 ✓, product 14 (not −14) ✗, both positive ✓.