SOLUTION: If the equation {{{sqrt(2)x^2 - sqrt(3)x + k = 0}}} with k a constant has two solutions {{{sin(theta)}}} and {{{cos(theta)}}} (0<=theta<=pi/2),then k = ... Hi, I got {{{3/4sqrt(

Question 1065005: If the equation with k a constant has two solutions and (0<=theta<=pi/2),then k = ...
Hi, I got . What should I do next? Do I need to pick some lesser number than that?
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
I agree that is necessary
to get two real solutions, and ,
but we need more than that,
and trying to use the quadratic formula seems awkward in this case.
I would say that it is necessary and sufficient
to have two real solutions, and ,
such that .
For any quadratic equation, we know that
if and are solutions to ,
.
In this case,
if and are solutions to ,
.
With , we would have , meaning and .
Let us see if we can find a out of
.
--> --> --> --> -->

NOTE:
The solutions to are
,
which correspond to

RELATED QUESTIONS
give the exact value of cos(theta) and tan(theta) if sin(theta)=(2/5) and 0 (answered by Fombitz)
Solve the equation sin(theta)+cos(theta)= 2(sin(theta)- cos(theta)), for 0 (answered by lwsshak3,KMST)
Question:find two values of theta that saitisfy each of the equations below. Give your... (answered by lwsshak3)
cos (theta-(3pi/4)) is equivalent to which of the following? a.... (answered by lwsshak3,Edwin McCravy)
Find the exact value of sin(theta) when tan(theta)= -1/ (2 sqrt 2) and cos(theta)>... (answered by lwsshak3)
solve the equation cos theta - tan theta * cos theta = 0 for 0< theta < 2... (answered by stanbon,DrBeeee)
solve the equation for 0◦≤ x ≤ 360◦ 4-sin theta= 4 cos ^2 theta.... (answered by stanbon)
A)write the equation cos(2 theta)-sin(theta)=0 in terms of sin (theta) B) Hence solve... (answered by stanbon)
Solve the equation 4sin^2(theta) + 2 cos(theta) = 3 for 0 < theta < 2... (answered by Theo)