Explanation

Let roots be r and r+2, since they differ by 2.

For x² + kx + 4 = 0:

1. Sum of roots = -b/a = -k → r + (r+2) = 2r + 2 = -k → r = (-k-2)/2

2. Product of roots = c/a = 4 → r(r+2) = 4

Plug r in: [(-k-2)/2] × [(-k-2)/2 + 2] = 4  

→ [(-k-2)/2] × [(2-k)/2] = 4  

→ (-k-2)(2-k) = 16

Simplify: k² - 4 = 16 → k² = 20 → k = ±2√5

So k can be 2√5 or -2√5.

Last verified 09-06-2026

Explanation

• π (pi) is an irrational number (cannot be written as a fraction).
• When we divide π by 3, it is still irrational.
• Irrational numbers are decimals that never end and never repeat.

Last verified on 08-06-2026

Explanation

-2x + 3 ≤ 9

Subtract 3: -2x ≤ 9 - 3 → -2x ≤ 6

Divide by -2. Rule: dividing by a negative flips the inequality sign  

x ≥ 6/(-2) → x ≥ -3

Last verified on 08-06-2026

Explanation

Use law of exponents: a^m · a^n = a^(m+n)

a^(x-1) · a^(x+1) = a^[(x-1) + (x+1)] = a^(2x)

Given a^(2x) = a^10

Bases are same, so exponents must be equal: 2x = 10

x = 10/2 = 5

Last verified on 08-06-2026

Explanation

Slope m = (y₂ - y₁)/(x₂ - x₁)

For a vertical line, x stays the same for all points → x₂ - x₁ = 0

So m = something / 0 → division by zero = undefined/infinite

Last verified on 08-06-2026