Question

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

Answer 1

Hey there !

Solution:

Given equation: x ( x - k ) = k + 1

=> x² - kx = k + 1

=> x² - kx - ( k + 1 ) = 0

This is of the form ax² + bx + c = 0, which is of the form of a quadratic equation.

Hence we know that, in a quadratic equation, Sum of all zeros or roots is equal to the Negative of  Coefficient of second term divided by the Coefficient of the first term.

That is,

$ax^2 - bx + c = 0, \\ \\ \implies \text{ Sum of roots} = \dfrac{ -b}{a}$

So here, the coefficient of second term is k and first term is 1.

Hence sum of all possible roots is:

Sum of roots = -k / 1 which is -k.

Hence the sum of all possible solutions is -k.

Hope my answer helped !

Answer 2

Step-by-step explanation:

hope this will help you