Find the value of K for which eqaution x squared minus k x minus 4 equals 0 has real roots

Asked by Divyaa | 25th Mar, 2017, 12:25: PM

Expert Answer:

begin mathsize 16px style Since space the space equation space straight x squared minus kx minus 4 equals 0 space is space given space to space have space real space roots comma
so comma space its space discriminant equals left parenthesis negative straight k right parenthesis squared minus 4 left parenthesis 1 right parenthesis left parenthesis negative 4 right parenthesis greater than 0 space space..... left parenthesis Using space straight b squared minus 4 ac greater than 0 space for space real space roots space property right parenthesis
rightwards double arrow straight k squared plus 16 greater than 0
rightwards double arrow straight k squared greater than negative 16
This space is space not space possible space since space we space have space root space of space straight a space negative space number comma space which space is space not space possible space for space real space numbers.

bold So bold space bold dear bold space bold student bold space bold please bold space bold note bold space bold that bold comma bold space bold the bold space bold equation bold space bold in bold space bold the bold space bold question bold space bold should bold space bold be bold space bold x to the power of bold 2 bold minus bold kx bold plus bold 4 bold equals bold 0 bold.
so comma space its space discriminant equals left parenthesis negative straight k right parenthesis squared minus 4 left parenthesis 1 right parenthesis left parenthesis 4 right parenthesis greater or equal than 0 space space..... left parenthesis Using space straight b squared minus 4 ac greater or equal than 0 space for space real space and space equal space roots space property right parenthesis
rightwards double arrow straight k squared minus 16 greater or equal than 0
rightwards double arrow straight k squared greater or equal than 16
rightwards double arrow straight k greater or equal than plus-or-minus 4
So comma space straight k equals 4 space or space straight k equals negative 4 space for space the space equation space to space have space real space and space equal space roots. end style

Answered by Rebecca Fernandes | 25th Mar, 2017, 05:49: PM