Quadratic Equations

A. -6, 3
B. 3, -2/3
C. -5, 2
D. -9, 2
3×2 – 9x + 2x – 6 = 0
3x(x – 3) + 2(x – 3) = 0
(x – 3)(3x + 2) = 0 => x = 3, -2/3

A. -6, 7
B. -8, 7
C. 14, -3
D. -7, 6
Explanation:
x2 + 7x – 6x + 42 = 0
x(x + 7) – 6(x + 7) = 0
(x + 7)(x – 6) = 0 => x = -7, 6

A. -2, -1/2
B. 4, -1
C. 4, 1
D. -2, 5/2
Explanation:
2×2 + 4x + x + 2 = 0
2x(x + 2) + 1(x + 2) = 0
(x + 2)(2x + 1) = 0 => x = -2, -1/2

A. If a > b
B. If a ≥ b
C. If a < b
D. If a ≤ b.
Explanation:
I. a2 – 13a + 42 = 0
=>(a – 6)(a – 7) = 0 => a = 6, 7
II. b2 – 15b + 56 = 0
=>(b – 7)(b – 8) = 0 => b = 7, 8
=>a ≤ b

A. If a > b
B. If a ≥ b
C. If a < b
D. If a ≤ b
Explanation:
a3 = 1331 => a = 11
b2 = 121 => b = ± 11
a ≥ b

A. If a > b
B. If a ≥ b
C. If a < b
D. If a ≤ b
Explanation:
I. 9a2 + 3a + 15a + 5 = 0
=>(3a + 5)(3a + 1) = 0 => a = -5/3, -1/3
II. 2b2 + 8b + 5b + 20 = 0
=>(2b + 5)(b + 4) = 0 => b = -5/2, -4
a is always more than b.
a > b.

A. If x < y
B. If x > y
C. If x ≤ y
D. If x ≥ y
Explanation:
I. x2 + 6x + 5x + 30 = 0
=>(x + 6)(x + 5) = 0 => x = -6, -5
II. y2 + 8y + 7y + 56 = 0
=>(y + 8)(y + 7) = 0 => y = -8, -7
=> x > y

A. If x < y
B. If x > y
C. If x ≤ y
D. If x ≥ y
E. If x = y or the relationship between x and y cannot be established.
Explanation:
I. x2 + 6x – 3x – 18 = 0
=>(x + 6)(x – 3) = 0 => x = -6, 3
II. y2 + 6y – 5y – 30 = 0
=>(y + 6)(y – 5) = 0 => y = -6, 5
No relationship can be established between x and y.

A. If x < y
B. If x > y
C. If x ≤ y
D. If x ≥ y
I. x2 + 4x + 5x + 20 = 0
=>(x + 4)(x + 5) = 0 => x = -4, -5
II. y2 + 3y + 2y + 6 = 0
=>(y + 3)(y + 2) = 0 => y = -3, -2
= x < y.

A. If x < y
B. If x > y
C. If x ≤ y
D. If x ≥ y
E. If x = y or the relationship between x and y cannot be established.
Explanation:
I. x2 – 7x + 6x – 42 = 0
=> (x – 7)(x + 6) = 0 => x = 7, -6
II. y2 – 8y – 9y + 72 = 0
=> (y – 8)(y – 9) = 0 => y = 8, 9
=> x < y