Find the value of x for which QE   x^2+kx+64=0 and  x^2-8x+k=0  both will have real roots

Asked by Fathima | 31st Mar, 2017, 05:31: PM

Expert Answer:

Dear student, you wrote find the value of x, which should be find the value of k.
Here is your solution:
begin mathsize 16px style Consider comma space the space first space equation.
Since space the space roots space are space real comma space
straight b squared minus 4 ac greater or equal than 0
rightwards double arrow straight k squared minus 4 left parenthesis 64 right parenthesis equals 0
rightwards double arrow straight k squared minus 256 equals 0
rightwards double arrow straight k squared equals 256
rightwards double arrow straight k equals plus-or-minus 16
Hence comma space straight k equals negative 16 space or space straight k equals 16. end style
 
Incase you have to still find the value of x, then do the above and continue with the following.
begin mathsize 16px style The space second space equation space becomes space straight x squared minus 8 straight x plus 16 equals 0 space or space straight x squared minus 8 straight x minus 16 equals 0 space.
On space factorising space each space of space the space equation comma space you space will space get space the space value space of space straight x.
end style

Answered by Rebecca Fernandes | 31st Mar, 2017, 09:19: PM