A seemingly tricky problem but NICEEEE!
Algebra
Level
pending
What is the sum of all possible solutions for x of the equation x ( x - k ) = k + 1?
1
k+1
k
0
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1 solution
Any quadratic equations in x with two roots a and b can be expressed as, (x - a)(x - b) = 0. Which on expansion takes the form, x² - (a + b)x - ab = 0
Hence, the sum of the roots = -(coefficient of x in the expanded form)
Now, x(x - k) = k + 1 => x² - kx - (k + 1) = 0
Hence, sum of the roots = -(-k) = k