Question

If the sum of the roots of the equation x to the power 2-x=lambda(2 x-1) is zero then lambda=

Answer 1

ʂƠƖŲɬıƠИ

the give equation is ....

$x {}^{2} - x = lambda(2x - 1) \\ = > x {}^{2} - x = 2x(lambda) - lambda \\ = > x {}^{2} - x - 2x(lambda) + lambda = 0 \\ = > x {}^{2} - (1 + 2lambda)x + lambda = 0 \\ \\ in \: this \: equation \: the \: sum \: of \: the \: roots \: is \\ = (1 + 2lambda) \\ and \: the \: product \: is = lambda$

now the sum of the roots is zero...

so ....

$(1 + 2lambda) = 0 \\ = > lambda = \frac{ - 1}{2}$

Hope this helps u....