Given equation: x^2 - 3kx + 4k^2 = 0.
Sum of roots = 3k, Product of roots = 4k^2.
Sum of squares of roots = (sum of roots)^2 - 2(product of roots)
= (3k)^2 - 2(4k^2)
= 9k^2 - 8k^2
= k^2.
Given sum of squares = one of the options.
If sum of squares = 1, then k^2 = 1, so k = ±1
Given equation:
x² - 5x + 6 = 0
Factor the quadratic equation:
(x - 2)(x - 3) = 0
This gives us:
x - 2 = 0 or x - 3 = 0
x = 2 or x = 3
The roots of the equation are x = 2 and x = 3.
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