An algebra problem by Nasir Haider

Algebra Level 3

What is the sum of all possible solutions for x x of the equation x ( x − k ) = k + 1 x ( x - k ) = k + 1 ?

1 1 2 k − 1 2k-1 k + 1 k+1 k k 0 0

Nasir Haider by Nasir Haider , 23, Pakistan

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1 solution

Nasir Haider
Apr 13, 2016

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

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