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1.
The roots of x² − 11x + 28 = 0 are:
Correct Answer: A [4 and 7]
Explanation:
Split: pq = 28, p + q = −11 → flip signs and divide by 1 → 4 and 7.
2.
The roots of 2x² − 9x + 10 = 0 are:
Correct Answer: B [2 and 5/2]
Explanation:
Split: pq = 20, p + q = −9 → flip signs and divide by 2 → 2 and 5/2.
3.
The sum of the roots of 3x² − 12x + 7 = 0 is:
Correct Answer: D [4]
Explanation:
Sum = −b/a = 12/3 = 4.
4.
The product of the roots of 5x² + 8x − 15 = 0 is:
Correct Answer: C [−3]
Explanation:
Product = c/a = −15/5 = −3.
5.
The roots of 4x² − 12x + 9 = 0 are:
Correct Answer: A [real and equal]
Explanation:
D = 144 − 4 × 4 × 9 = 0 → two equal roots, each 12/8 = 3/2.
6.
The discriminant of 2x² + 5x − 3 = 0 is:
Correct Answer: B [49]
Explanation:
D = b² − 4ac = 25 − 4 × 2 × (−3) = 25 + 24 = 49.
7.
Which equation has the roots 3 and −5?
Correct Answer: D [x² + 2x − 15 = 0]
Explanation:
x² − (sum)x + product = 0: sum −2, product −15 → x² + 2x − 15 = 0.
8.
Both roots of x² + 13x + 42 = 0 are:
Correct Answer: C [negative]
Explanation:
Sign Rule: b and c both positive → both roots negative (−6, −7).
9.
One root of x² + kx + 48 = 0 is −6. The value of k is:
Correct Answer: B [14]
Explanation:
Product 48 → other root = 48/(−6) = −8.
10.
The values of x that satisfy x² = 196 are:
Correct Answer: A [14 and −14]
Explanation:
x² = k has two roots ±√k → ±14.
11.
Which equation does NOT have both roots positive?
Correct Answer: C [x² + 2x − 15 = 0]
Explanation:
c < 0 in x² + 2x − 15 → roots of opposite signs (3, −5); the others have b negative, c positive → both positive.
12.
The roots of 6x² − x − 2 = 0 are:
Correct Answer: D [−1/2 and 2/3]
Explanation:
Split: pq = −12, p + q = −1 → flip signs and divide by 6 → −1/2 and 2/3.
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