Find the value of k, if the sum of the square of the roots of x² - 3kx + 4k² = 0 is equal to ______?
- ±1
- ±2
- ±4
- None of these
Explanation
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
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