Quadratic Equations with Parameters

Submitted by ladislav.foltyn on Sat, 04/20/2019 - 13:43
Project ID: 
6000000056
Accepted: 
SubArea: 
Quadratic equations and inequalities
Type: 
Match
Layout: 
6x6
Question: 
The equations with variable $x$ and parameter $m$ are given. For every equation find such set of all possible values of $m$, that the given equation has exactly one solution.
Questions Title: 
Equations:
Answers Title: 
Sets of values of parameter $m$:
Question 1: 
$x^2+2mx+4=0$
Answer 1: 

$\{-2;2\}$

Question 2: 
$mx^2-2x+m=0$
Answer 2: 

$\{-1;0;1\}$

Question 3: 
$4(x+m)^2=x^2+m$
Answer 3: 

$\left\{0;-\frac34\right\}$

Question 4: 
$x^2m+4=3(m+2)$
Answer 4: 

$\left\{-\frac23\right\}$

Question 5: 
$2x^2+3xm+2=0$
Answer 5: 

$\left\{-\frac43;\frac43\right\}$

Question 6: 
$x^2-2mx+1=0$
Answer 6: 

$\{-1;1\}$

Tex: 
%tiket 32823 \NastavOT{2} \NastavOD{3}