Quadratic Equations - Real & Equal Roots

Explanatory Answer

i. 2x² + kx + 3 = 0

The two roots of a quadratic equation ax² + bx + c = 0 are real and equal if its discriminant b² – 4ac = 0
In this equation a = 2, b = k and c = 3
∴ b² – 4ac = k² - 4 × 2 × 3 = 0
k² - 24 = 0
k = ±\\sqrt{24}) = ±2\\sqrt{6})

ii. kx(x - 2) + 6 = 0

kx² – 2kx + 6 = 0
The two roots of a quadratic equation ax² + bx + c = 0 are real and equal if its discriminant b² – 4ac = 0
In this equation a = k, b = -2k and c = 6
∴ b² - 4ac = (-2k)² - 4 × k × 6 = 0
4k² - 24k = 0
Divide the equation by 4: k² - 6k = 0
k(k - 6) = 0
So k = 0 or k = 6
If k = 0 the quadratic equation will not exist.
∴ k = 6